Load libraries and functions

 # install.packages("INLA",repos=c(getOption("repos"),INLA="https://inla.r-inla-download.org/R/stable"), dep=TRUE) 
tictoc::tic()

library(INLA)          # For fitting integrated nested Laplace approximation (INLA) models
library(tidyverse)     # For data manipulation and visualization
library(sp)            # For spatial data handling
library(spdep)         # For spatial dependence analysis
library(flextable)     # For creating flexible tables
library(RColorBrewer)  # For color palettes
library(rcartocolor)   # For additional color palettes
library(cowplot)       # For combining plots
library(janitor)       # For cleaning data
library(broom)

# Functions ---------------------------------------------------------------

# Standardize a numeric vector
my_std <- function(x) { (x - mean(x,na.rm=TRUE)) / sd(x,na.rm = TRUE)}

# Fit a BYM2 model using INLA
fit_bym2 <- function(table,
                     outcome_var,
                     interest_var,
                     distribution = "poisson",
                     formula_terms = NULL,
                     prec_param =  c(1, 0.001),
                     phi_param = c(0.5, 0.5)) {

# Define priors for precision and phi
    prior <- list(
  prec = list(
    prior = "pc.prec",
    param = prec_param),
  phi = list(
    prior = "pc",
    param = phi_param)
  )
    
  # Construct the INLA formula based on input parameters
  if (is.null(formula_terms)) {
    inla_formula <- as.formula(paste(outcome_var, "~", interest_var, "+ f(ui, model = 'bym2', graph = g, hyper = prior, adjust.for.con.comp = TRUE,
constr = TRUE, scale.model = TRUE)"))
  } else {
    inla_formula <- as.formula(paste(outcome_var, "~", interest_var, "+", formula_terms, "+ f(ui, model = 'bym2', graph = g, hyper = prior, adjust.for.con.comp = TRUE,
constr = TRUE, scale.model = TRUE)"))
  }
    
    
    
#adjust.for.con.comp = TRUE, scale.model = TRUE:  assigns one intercept to each region in addition to using a sum-to-zero constraint for each connected region. By adding an intercept for each region, we infer that the baseline prevalence is different in the disconnected regions.
#The spatial random effects can be interpreted as the area-specific deviation from the region-specific risk in this case. The intercepts for the disconnected regions need to be explicitly specified in INLA:

  
  # Fit the INLA model with BYM2 prior
fit <- inla(inla_formula,
              data = table,
              family = distribution,
              control.compute = list(dic = TRUE, waic = TRUE,cpo=TRUE,config=TRUE),
              control.predictor = list(compute = TRUE),
              verbose = FALSE)
  
  # Return the INLA model object
  return(fit)
}

# Tidy up INLA model fixed effects results
tidy_inla <- function(fixed_effects, exponentiate = FALSE, sigfig =NULL) {
  # Create a tidy data frame
  tidy_results <- fixed_effects %>%
    dplyr::rename(estimate = 'mean',
                  std.error = 'sd',
                  lower_ci = '0.025quant',
                  upper_ci = '0.975quant')
  
  if (exponentiate) {
    tidy_results <- tidy_results %>%
      mutate(estimate = exp(estimate),
             lower_ci = exp(lower_ci),
             upper_ci = exp(upper_ci))
  }
  
  if (!is.null(sigfig)) {
    tidy_results <- tidy_results %>%
      mutate(estimate = signif(estimate, sigfig),
             std.error = signif(std.error, sigfig),
             lower_ci = signif(lower_ci, sigfig),
             upper_ci = signif(upper_ci, sigfig))
  }
  
  return(tidy_results)
}

# prs <- function(x,n.dig = 2){
#   
#   formatC(round(x,n.dig), format='f', big.mark = ",",digits = n.dig)
#   
# }

cma_models <- function(cma_data,
                       cma_name,
                       outcome,
                       deprivation_indicator,
                       distribution = "poisson") {
  ### 0: Unadjusted non=spatial
  print("Fit unadjusted non-spatial")
  
  m0 <- inla(
    as.formula(paste(
      outcome, "~", deprivation_indicator, "+ f(ui, model = 'iid')"
    )),
    data = cma_data,
    family = distribution,
    control.compute = list(
      dic = TRUE,
      waic = TRUE,
      cpo = TRUE,
      config = TRUE
    ),
    control.predictor = list(compute = TRUE),
    verbose = FALSE
  )
  
  m0_fe <- tidy_inla(m0$summary.fixed,
                     exponentiate = TRUE,
                     sigfig = 3) %>%
    mutate(
      `IRR (95% CI)` = paste0(estimate, " (", lower_ci, ", ", upper_ci, ")"),
      variable = row.names(.)
    ) %>%
    select(variable, `IRR (95% CI)`)
  
  ###### Spatial Models #####
  
  ### 1: Unadjusted
  
  print("Fit unadjusted")
  
  m1 <- fit_bym2(cma_data, outcome, deprivation_indicator, distribution)
  m1_fe <- tidy_inla(m1$summary.fixed,
                     exponentiate = TRUE,
                     sigfig = 3) %>%
    mutate(
      `IRR (95% CI)` = paste0(estimate, " (", lower_ci, ", ", upper_ci, ")"),
      variable = row.names(.)
    ) %>%
    select(variable, `IRR (95% CI)`)
  
  print("Fit adjusted by road length")
  
  ### 2: Adjusted by Road Length
  m2 <- fit_bym2(cma_data,
                 outcome,
                 deprivation_indicator,
                 formula_terms = "ln_roads_km_c",
                 distribution)
  m2_fe <- tidy_inla(m2$summary.fixed,
                     exponentiate = TRUE,
                     sigfig = 3) %>%
    mutate(
      `IRR (95% CI)` = paste0(estimate, " (", lower_ci, ", ", upper_ci, ")"),
      variable = row.names(.)
    ) %>%
    select(variable, `IRR (95% CI)`)
  
  ### 3: Adjusted by Road Length and other variables
  m3 <- fit_bym2(cma_data,
                 outcome,
                 deprivation_indicator,
                 formula_terms = "ln_roads_km_c + roads_prop_highway_arterial_z + ale_index_z + canbics_index_z + population_100_c",
                 distribution)
  m3_fe <- tidy_inla(m3$summary.fixed,
                     exponentiate = TRUE,
                     sigfig = 3) %>%
    mutate(
      `IRR (95% CI)` = paste0(estimate, " (", lower_ci, ", ", upper_ci, ")"),
      variable = row.names(.)
    ) %>%
    select(variable, `IRR (95% CI)`)
  
  l <- list(m0, m1, m2, m3)
  names(l) <- c("Nonspatial","Unadjusted", "Adjusted1", "Adjusted2")
  
  print("Fit adjusted by road length and covariates")
  
  
  # Compile results into a tibble
  tibble(
    cma = cma_name,
    model_type = c("Nonspatial","unadjusted", "adjusted_minimal", "adjusted_full"),
    models = l,
    fixed_effects = list(m0_fe, m1_fe, m2_fe, m3_fe)
  )
  
}


# Clean and format fixed effects results from models
clean_fixed_effects <- function(cma_model_object){
  
  cma_model_object %>% 
    bind_rows(,.id="model_type") %>% 
    mutate(model_type = case_when(model_type == "1"~"Nonspatial Unadjusted IRR (95% CI)",
                                  model_type == "2"~"Spatial Unadjusted IRR (95% CI)",
                                  model_type == "3"~"Spatial Minimally Adjusted IRR (95% CI)",
                                  model_type == "4"~"Spatial Adjusted IRR (95% CI)"
                                  
    )) %>% 
    pivot_wider(id_cols = variable,names_from = model_type,values_from = `IRR (95% CI)` ) %>% 
    mutate(variable = case_when(variable == "ln_roads_km_c" ~"Log(Total KMs of Road)",
                                variable == "roads_prop_highway_arterial_z" ~ "% of roads classifed as Arterial/Highway (SD)",
                                variable == "ale_index_z" ~ "Canadian Active Living Enrivonment Index (SD)",
                                variable == "canbics_index_z" ~ "Canadian Bikeway Safety and Comfort Index (SD)",
                                variable == "population_100_c" ~ "Population (100)",
                                TRUE ~ variable
                                
    )) 
  
}


assign_nearest_neighbors <- function(nb_object, sp_object,make_symmetrical=TRUE) {
    # Calculate centroids for isolated polygons
  centroids <- coordinates(sp_object)  # If using sp
  
  centroids_nn <- knearneigh(centroids, k = 3)

  # Get the list of neighbors
  zero_nb_logical <- sapply(nb_object, function(x) x[1] ==0)
  
  zero_nb_indices <- which(zero_nb_logical)
  
  zero_nn <- centroids_nn$nn[zero_nb_indices, ]
  
  for(i in 1:length(zero_nn)){
    
    nb_object[zero_nb_indices[i]] <- zero_nn[i]
  }
  
  if(make_symmetrical==TRUE){
    
    nb_object <- make.sym.nb(nb_object)
  }
  
  
  return(nb_object)
}

create_descriptive_table <- function(sf_obj, selected_vars) {
  sf_obj %>%
    # Drop geometry and select only the specified variables
    st_drop_geometry() %>%
    select(all_of(selected_vars)) %>%
    # Gather descriptive statistics for each variable
    summarise(across(everything(), list(
      sum = ~sum(.x, na.rm = TRUE),
      mean = ~mean(.x, na.rm = TRUE),
      sd = ~sd(.x, na.rm = TRUE),
      min = ~min(.x, na.rm = TRUE),
      max = ~max(.x, na.rm = TRUE),
      n = ~sum(!is.na(.x)|is.na(.x)),       # Count non-NA values
      missing = ~sum(is.na(.x)),
      n_zero = ~sum(.x==0,na.rm=TRUE)# Count 0 values
    ), .names = "{.col}-{.fn}")) %>%
    # Pivot longer to have each variable as its own row
    pivot_longer(everything(), 
                 names_to = c("variable", ".value"),
                 names_sep = "-") %>%
    # Add a column to identify the sf object
    # Reorder columns for better readability
    select(variable, n, sum, mean, sd, min, max, , missing,n_zero)
}

Load Data and Clean

# Load and clean census data for Canadian metropolitan areas (CMA)
cma_name <- cancensus::get_census("CA21",
                                  level = "CMA",
                                  regions = list(PR=59)) %>% 
  rename(CMA_UID = GeoUID,  # Rename GeoUID to CMA_UID for clarity
         `CMA Name` = `Region Name`,  # Rename 'Region Name' to 'CMA Name'
         cma_population = Population) %>%  # Rename 'Population' to 'cma_population'
  arrange(desc(cma_population)) %>%  # Sort by population in descending order
  select(CMA_UID, Type, `CMA Name`, cma_population) %>%  # Select relevant columns
  mutate(`CMA Name` = str_remove_all(`CMA Name`, " \\(B\\)|\\(K\\)|\\(D\\)")) %>%  # Remove labels (B, K, D) from names
  clean_names() %>%  # Clean column names (lowercase and snake_case)
  mutate(cma_name = stringr::str_trim(cma_name, "right"))  # Trim whitespace from the right
## Downloading: 920 B     Downloading: 920 B     Downloading: 920 B     Downloading: 920 B     Downloading: 920 B     Downloading: 920 B
# Read spatial data for dissemination areas in British Columbia
bc_da <- st_read(
  "C:/Users/micha/Documents/GitHub/Area-Level-Deprivation-Traffic-Injury/Processed Data/da_v3_2021.gpkg"
) %>%
  # Join the census data with the spatial data
  left_join(cma_name, by = join_by(cma_uid)) %>%
  filter(!is.na(cma_name)) %>%  # Filter out rows without CMA names
  mutate(
    population_100 = population / 100,  # Scale population down by 100
    population_100_c = scale(population_100, scale = FALSE),  # Center population
    total_roads_km = total_roads_m / 1000,  # Convert road lengths from meters to kilometers
    
    # Calculate casualty claims rates per kilometer of road
    n_casualty_claims_rate = n_casualty_claims / total_roads_km * 10,
    n_pedestrian_casualty_claims_rate = n_pedestrian_casualty_claims / total_roads_km * 10,
    n_cyclist_casualty_claims_rate = n_cyclist_casualty_claims / total_roads_km * 10,

    # Calculate the proportion of roads that are highways or arterials
    roads_prop_highway_arterial = (highway_m + arterial_m) / total_roads_m,
    roads_prop_highway_arterial_z = my_std(roads_prop_highway_arterial),  # Standardize the proportion
    
    # Log-transform the total length of roads in kilometers
    ln_roads_km = ifelse(total_roads_km == 0, NA, log(total_roads_km)),
    ln_roads_km_c = scale(ln_roads_km, scale = FALSE),  # Center log-transformed roads
    
    # Calculate casualty claims rates by total road kilometers
    casualty_claims_rate = n_casualty_claims / total_roads_km * 10,
    cyclist_casualty_claims_rate = n_cyclist_casualty_claims / total_roads_km * 10,
    pedestrian_casualty_claims_rate = n_pedestrian_casualty_claims / total_roads_km * 10,

    # Convert CANBICS class to descriptive categories
    canbics_class_c = case_when(
      canbics_class == 1 | canbics_class == "2" ~ "1 - Low",
      canbics_class == 5 | canbics_class == "4" ~ "3 - High",
      canbics_class == 3 ~ "2 - Medium"
    ),
    canbics_index_z = my_std(canbics_index),  # Standardize CANBICS index
    
    # Convert ALE class to descriptive categories
    ale_class_c = case_when(
      ale_class == 1 | ale_class == "2" ~ "1 - Low",
      ale_class == 5 | ale_class == "4" ~ "3 - High",
      ale_class == 3 ~ "2 - Medium"
    ),
    ale_index_z = my_std(ale_index),  # Standardize ALE index
    
    # Calculate VanDIX score based on various factors
    z_no_highschool_prevalance_w = scale(no_highschool_prevalance),
    z_university_degree_prevalance_w = scale(university_degree_prevalance * -1),
    z_unemployment_rate_w = scale(unemployment_rate),
    z_lone_parent_fam_prevalence_w = scale(lone_parent_fam_prevalence),
    z_hh_avg_income_w = scale(hh_avg_income * -1),
    z_home_owner_prevalence_w = scale(home_owner_prevalence * -1),
    z_participation_rate_w = scale(participation_rate * -1),
    
    # Compute VanDIX (Area Level Deprivation Index) score
    vandix = as.numeric(
      z_hh_avg_income_w * 0.089 +
        z_home_owner_prevalence_w * 0.089 +
        z_lone_parent_fam_prevalence_w * 0.143 +
        z_no_highschool_prevalance_w * 0.25 +
        z_university_degree_prevalance_w * 0.179 +
        z_unemployment_rate_w * 0.214 +
        z_participation_rate_w * 0.036
    ),
    
    vandix_z = my_std(vandix),
    
    # Categorize the standardized VanDIX score
    vandix_z_c = case_when(
      vandix_z < -5 ~ "<-5",
      vandix_z >= -5 & vandix_z < -4 ~ "-5 - -4",
      vandix_z >= -4 & vandix_z < -3 ~ "-4 - -3",
      vandix_z >= -3 & vandix_z < -2 ~ "-3 - -2",
      vandix_z >= -2 & vandix_z < -1 ~ "-2 - -1",
      vandix_z >= -1 & vandix_z < 0 ~ "-1 - 0",
      vandix_z >= 0 & vandix_z < 1 ~ "0 - 1",
      vandix_z >= 1 & vandix_z < 2 ~ "1 - 2",
      vandix_z >= 2 & vandix_z < 3 ~ "2 - 3",
      vandix_z >= 3 & vandix_z < 4 ~ "3 - 4",
      vandix_z >= 4 & vandix_z < 5 ~ "4 - 5",
      vandix_z >= 5 ~ ">5"
    ),
    
    # Convert the VanDIX categories into a factor for ordered plotting
    vandix_z_c = factor(vandix_z_c, levels = c("<-5", "-5 - -4", "-4 - -3", "-3 - -2", "-2 - -1", "-1 - 0", "0 - 1", "1 - 2", "2 - 3", "3 - 4", "4 - 5", ">5"))
  ) %>% 
  # Assign regions based on CMA names
  mutate(region_name = case_when(
    cma_name %in% c("Prince Rupert", "Terrace") ~ "Northwest",
    cma_name %in% c("Fort St. John", "Dawson Creek", "Prince George", "Quesnel", "Williams Lake") ~ "North Central",
    cma_name %in% c("Kamloops", "Salmon Arm") ~ "Kamloops-Salmon Arm",
    cma_name %in% c("Vernon", "Kelowna", "Penticton") ~ "Okanagan",
    cma_name %in% c("Cranbrook", "Nelson", "Trail") ~ "Southeast",
    cma_name %in% c("Vancouver", "Squamish") ~ "Vancouver-Squamish",
    cma_name %in% c("Abbotsford - Mission", "Chilliwack") ~ "Fraser Valley",
    cma_name %in% c("Campbell River", "Courtenay", "Port Alberni", "Parksville", "Nanaimo", "Ladysmith", "Duncan", "Powell River") ~ "Central Island-Powell River",
    cma_name == "Victoria" ~ "Victoria",
    TRUE ~ NA_character_  # Handle cases where CMA name doesn't match any of the specified values
  ))
## Reading layer `da_v3_2021' from data source 
##   `C:\Users\micha\Documents\GitHub\Area-Level-Deprivation-Traffic-Injury\Processed Data\da_v3_2021.gpkg' 
##   using driver `GPKG'
## Simple feature collection with 7848 features and 130 fields
## Geometry type: MULTIPOLYGON
## Dimension:     XY
## Bounding box:  xmin: 273876.1 ymin: 367780.7 xmax: 1870608 ymax: 1735671
## Projected CRS: NAD83 / BC Albers
# bc_da %>% 
#   filter(total_roads_km==0) %>% 
#   nrow()

bc_da <- bc_da %>% 
  filter(total_roads_km>0) #filter out DAs without any roads


# Split the data into a list of CMAs
bc_cma <- bc_da %>% 
  split(.$cma_name)

# Split the data into a list of regions
bc_region <- bc_da %>% 
  split(.$region_name)

# Summarize population data for each CMA
cma_pop <- bc_da %>%
  st_drop_geometry() %>%  # Remove geometry for summarization
  group_by(cma_name) %>% 
  summarise(n_da = n(),  # Count the number of dissemination areas
            population = sum(population, na.rm = TRUE)) %>% 
  arrange(desc(population))  # Sort by population

# Summarize population data for each region
region_pop <- bc_da %>%
  st_drop_geometry() %>%  # Remove geometry for summarization
  group_by(region_name) %>% 
  summarise(n_da = n(),  # Count the number of dissemination areas
            population = sum(population, na.rm = TRUE)) %>% 
  arrange(desc(population))  # Sort by population

# Create descriptive tables for each region
region_descriptives <- map(
  bc_region,
  create_descriptive_table,
  c(
    "n_claims",
    "n_casualty_claims",
    "n_cyclist_claims",
    "n_cyclist_casualty_claims",
    "n_pedestrian_claims",
    "n_pedestrian_casualty_claims",
    "population",
    "total_roads_km",
    "roads_prop_highway_arterial",
    "no_highschool_prevalance",
    "unemployment_rate",
    "hh_avg_income",
    "participation_rate",
    "university_degree_prevalance",
    "lone_parent_fam_prevalence",
    "home_owner_prevalence",
    "vandix",
    "roads_prop_highway_arterial",
    "ale_index",
    "canbics_index"
  )
) %>% 
  bind_rows(.id = "region") %>% 
  arrange(desc(n)) %>%  # Sort by count
  mutate(p_zero = n_zero / n * 100)  # Calculate percentage of zero claims

# Create descriptive tables for each CMA
cma_descriptives <- map(
  bc_cma,
  create_descriptive_table,
  c(
    "n_claims",
    "n_casualty_claims",
    "n_cyclist_claims",
    "n_cyclist_casualty_claims",
    "n_pedestrian_claims",
    "n_pedestrian_casualty_claims",
    "population",
    "total_roads_km",
    "roads_prop_highway_arterial",
    "no_highschool_prevalance",
    "unemployment_rate",
    "hh_avg_income",
    "participation_rate",
    "university_degree_prevalance",
    "lone_parent_fam_prevalence",
    "home_owner_prevalence",
    "vandix",
    "roads_prop_highway_arterial",
    "ale_index",
    "canbics_index"
  )
) %>% 
  bind_rows(.id = "cma") %>% 
  arrange(desc(n)) %>%  # Sort by count
  mutate(p_zero = n_zero / n * 100)  # Calculate percentage of zero claims

Missing Data

missing_data <- bc_da %>% 
  filter(is.na(vandix_z)|is.na(canbics_index_z)|is.na(ale_index_z)|total_roads_km==0|is.na(population))

nrow(missing_data)
## [1] 820
nrow(missing_data)/nrow(bc_da)
## [1] 0.1266801
create_descriptive_table(missing_data,
  c(
    "n_claims",
    "n_casualty_claims",
    "n_cyclist_claims",
    "n_cyclist_casualty_claims",
    "n_pedestrian_claims",
    "n_pedestrian_casualty_claims",
    "population",
    "total_roads_km",
    "roads_prop_highway_arterial",
    "no_highschool_prevalance",
    "unemployment_rate",
    "hh_avg_income",
    "participation_rate",
    "university_degree_prevalance",
    "lone_parent_fam_prevalence",
    "home_owner_prevalence",
    "roads_prop_highway_arterial",
    "vandix_z",
    "ale_index_z",
    "canbics_index_z"
  )) %>% 
  mutate(
    complete = n- missing,
    p_missing = missing/n*100,
         
         ) %>% 
  select(variable,n,complete,missing,p_missing,everything()) %>% 
     flextable() %>% 
      merge_v(j = ~  + n ) %>% 
   theme_booktabs() %>% 
   colformat_double(
  big.mark = ",", digits = 1, na_str = "N/A"
) 

variable

n

complete

missing

p_missing

sum

mean

sd

min

max

n_zero

n_claims

820

820

0

0.0

123,572.0

150.7

301.5

0.0

3,234.0

49

n_casualty_claims

820

0

0.0

24,831.0

30.3

63.5

0.0

649.0

111

n_cyclist_claims

820

0

0.0

1,519.0

1.9

6.7

0.0

115.0

500

n_cyclist_casualty_claims

820

0

0.0

988.0

1.2

4.5

0.0

72.0

567

n_pedestrian_claims

820

0

0.0

1,657.0

2.0

5.3

0.0

56.0

454

n_pedestrian_casualty_claims

820

0

0.0

1,252.0

1.5

3.8

0.0

39.0

478

population

817

3

0.4

553,045.0

676.9

709.0

0.0

8,739.0

35

total_roads_km

820

0

0.0

9,193.1

11.2

25.3

0.0

286.0

0

roads_prop_highway_arterial

820

0

0.0

140.3

0.2

0.2

0.0

1.0

340

no_highschool_prevalance

234

586

71.5

48.9

0.2

0.1

0.0

0.8

10

unemployment_rate

234

586

71.5

2,269.4

9.7

9.8

0.0

60.0

57

hh_avg_income

105

715

87.2

8,304,484.0

79,090.3

22,810.6

38,632.0

158,248.0

0

participation_rate

234

586

71.5

14,203.2

60.7

14.7

0.0

94.6

1

university_degree_prevalance

234

586

71.5

116.2

0.5

0.1

0.0

0.8

1

lone_parent_fam_prevalence

236

584

71.2

41.9

0.2

0.2

0.0

1.0

19

home_owner_prevalence

234

586

71.5

173.5

0.7

0.3

0.0

1.3

9

vandix_z

103

717

87.4

8.6

0.1

0.9

-1.6

3.2

0

ale_index_z

140

680

82.9

-38.5

-0.3

1.1

-0.9

6.2

0

canbics_index_z

169

651

79.4

-52.9

-0.3

0.9

-0.9

4.4

0

Spatial Models

Vancouver - Squamish

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

Vancouver-Squamish

n_claims

3,620

693,530.0

191.6

363.3

0.0

6,315.0

0

10

0.3

n_casualty_claims

149,692.0

41.4

84.8

0.0

1,896.0

0

131

3.6

n_cyclist_claims

7,656.0

2.1

4.7

0.0

115.0

0

1,455

40.2

n_cyclist_casualty_claims

4,968.0

1.4

3.2

0.0

72.0

0

1,857

51.3

n_pedestrian_claims

9,539.0

2.6

5.1

0.0

80.0

0

1,288

35.6

n_pedestrian_casualty_claims

7,502.0

2.1

4.0

0.0

68.0

0

1,456

40.2

population

2,667,057.0

737.0

532.2

0.0

8,800.0

1

8

0.2

total_roads_km

15,056.8

4.2

5.8

0.0

176.7

0

0

0.0

roads_prop_highway_arterial

577.0

0.2

0.2

0.0

1.0

0

1,426

39.4

no_highschool_prevalance

476.5

0.1

0.1

0.0

0.8

298

16

0.4

unemployment_rate

19,517.2

5.9

3.6

0.0

40.0

298

339

9.4

hh_avg_income

279,328,113.0

85,421.4

34,171.3

0.0

560,267.0

350

3

0.1

participation_rate

215,750.1

64.9

10.1

0.0

94.6

298

1

0.0

university_degree_prevalance

1,890.5

0.6

0.1

0.1

1.0

298

0

0.0

lone_parent_fam_prevalence

513.7

0.2

0.1

0.0

0.7

297

15

0.4

home_owner_prevalence

2,229.1

0.7

0.2

0.0

1.3

298

36

1.0

vandix

-473.2

-0.1

0.6

-2.1

3.9

350

0

0.0

ale_index

5,407.4

1.6

3.6

-2.1

25.1

308

13

0.4

canbics_index

15,159.2

4.6

4.1

0.0

24.3

303

72

2.0

Maps

claims <- ggplot() + 
  geom_sf(data = vancouver_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = vancouver_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = vancouver_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

vancouver_sp <- as(vancouver_sf, "Spatial")
vancouver_sp$ui <- 1:nrow(vancouver_sp@data)

coords <- coordinates(vancouver_sp)
vancouver_nb <- poly2nb(vancouver_sp, queen = TRUE)
## Warning in poly2nb(vancouver_sp, queen = TRUE): neighbour object has 5 sub-graphs;
## if this sub-graph count seems unexpected, try increasing the snap argument.
vancouver_nb
## Neighbour list object:
## Number of regions: 3620 
## Number of nonzero links: 22970 
## Percentage nonzero weights: 0.1752846 
## Average number of links: 6.345304 
## 5 disjoint connected subgraphs
#assign nearest neighbour for no links

vancouver_nb <- assign_nearest_neighbors(vancouver_nb,vancouver_sp)

plot(vancouver_sp, border = grey(0.5))
plot(vancouver_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(vancouver_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(vancouver_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  vancouver_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 24.44, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      2.317291e-01     -2.763194e-04      9.011585e-05
cyc_cc_mi <- moran.test(vancouver_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  vancouver_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 38.937, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      3.682520e-01     -2.763194e-04      8.957925e-05
pd_cc_mi <- moran.test(vancouver_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  vancouver_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 32.697, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      3.121578e-01     -2.763194e-04      9.130404e-05

BYM2 Models

nb2INLA("vancouver.adj", vancouver_nb)
g <- inla.read.graph(filename = "vancouver.adj")


# Model Set 1: Total Casualty Claim Crashes

van_models_1 <- cma_models(cma_data = vancouver_sp@data, cma_name = "Vancouver-Squamish",outcome =  "n_casualty_claims", deprivation_indicator = "vandix_z",distribution = "poisson") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
van_all <- clean_fixed_effects(van_models_1$fixed_effects)

map(van_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.384, Running = 1.27, Post = 0.245, Total = 1.9 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 2.852 0.024      2.804    2.852      2.899 2.852   0
## vandix_z    0.407 0.027      0.354    0.407      0.460 0.407   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.536 0.014      0.508    0.536      0.564 0.535
## 
## Deviance Information Criterion (DIC) ...............: 23972.24
## Deviance Information Criterion (DIC, saturated) ....: 7523.23
## Effective number of parameters .....................: 3482.99
## 
## Watanabe-Akaike information criterion (WAIC) ...: 23973.60
## Effective number of parameters .................: 2395.12
## 
## Marginal log-Likelihood:  -16493.76 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 21.3, Running = 4.93, Post = 0.722, Total = 27 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 2.804 0.016      2.773    2.804      2.836 2.804   0
## vandix_z    0.204 0.033      0.139    0.204      0.269 0.204   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.311 0.014      0.285    0.311      0.340 0.311
## Phi for ui       0.793 0.021      0.749    0.794      0.832 0.795
## 
## Deviance Information Criterion (DIC) ...............: 23815.04
## Deviance Information Criterion (DIC, saturated) ....: 7366.01
## Effective number of parameters .....................: 3418.92
## 
## Watanabe-Akaike information criterion (WAIC) ...: 23708.89
## Effective number of parameters .................: 2287.15
## 
## Marginal log-Likelihood:  -15034.86 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 22, Running = 5.28, Post = 0.933, Total = 28.2 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   3.254 0.015      3.224    3.254      3.284 3.254   0
## vandix_z      0.315 0.026      0.264    0.315      0.366 0.315   0
## ln_roads_km_c 1.291 0.029      1.234    1.291      1.348 1.291   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.507 0.020      0.469    0.507      0.547 0.506
## Phi for ui       0.810 0.016      0.777    0.810      0.840 0.811
## 
## Deviance Information Criterion (DIC) ...............: 23704.56
## Deviance Information Criterion (DIC, saturated) ....: 7255.51
## Effective number of parameters .....................: 3265.09
## 
## Watanabe-Akaike information criterion (WAIC) ...: 23512.58
## Effective number of parameters .................: 2154.27
## 
## Marginal log-Likelihood:  -14247.28 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 22.6, Running = 5.48, Post = 0.845, Total = 28.9 
## Fixed effects:
##                                mean    sd 0.025quant 0.5quant 0.975quant  mode
## (Intercept)                   2.989 0.017      2.956    2.989      3.022 2.989
## vandix_z                      0.216 0.022      0.174    0.216      0.258 0.216
## ln_roads_km_c                 0.987 0.027      0.934    0.987      1.040 0.987
## roads_prop_highway_arterial_z 0.595 0.016      0.563    0.595      0.626 0.595
## ale_index_z                   0.111 0.037      0.037    0.111      0.184 0.111
## canbics_index_z               0.210 0.037      0.137    0.209      0.282 0.209
## population_100_c              0.017 0.003      0.012    0.017      0.022 0.017
##                               kld
## (Intercept)                     0
## vandix_z                        0
## ln_roads_km_c                   0
## roads_prop_highway_arterial_z   0
## ale_index_z                     0
## canbics_index_z                 0
## population_100_c                0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.838 0.038      0.766    0.837      0.915 0.836
## Phi for ui       0.777 0.022      0.732    0.777      0.817 0.779
## 
## Deviance Information Criterion (DIC) ...............: 23557.65
## Deviance Information Criterion (DIC, saturated) ....: 7108.60
## Effective number of parameters .....................: 3108.54
## 
## Watanabe-Akaike information criterion (WAIC) ...: 23292.03
## Effective number of parameters .................: 2020.13
## 
## Marginal log-Likelihood:  -13604.82 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

van_models_2 <- cma_models(vancouver_sp@data,"Vancouver-Squamish","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
van_cyclist <- clean_fixed_effects(van_models_2$fixed_effects)

map(van_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.193, Running = 1.09, Post = 0.407, Total = 1.69 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.616 0.043     -0.704   -0.615     -0.534 -0.615   0
## vandix_z     0.028 0.032     -0.035    0.028      0.091  0.028   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant mode
## Precision for ui 0.632 0.029      0.577    0.631       0.69 0.63
## 
## Deviance Information Criterion (DIC) ...............: 10994.39
## Deviance Information Criterion (DIC, saturated) ....: 6440.89
## Effective number of parameters .....................: 2464.49
## 
## Watanabe-Akaike information criterion (WAIC) ...: 12145.92
## Effective number of parameters .................: 2387.64
## 
## Marginal log-Likelihood:  -5594.29 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 21.4, Running = 4.24, Post = 0.538, Total = 26.2 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.522 0.032     -0.587   -0.522     -0.459 -0.522   0
## vandix_z     0.142 0.037      0.069    0.142      0.216  0.142   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.567 0.042      0.489    0.565      0.654 0.562
## Phi for ui       0.633 0.048      0.534    0.635      0.724 0.638
## 
## Deviance Information Criterion (DIC) ...............: 9763.24
## Deviance Information Criterion (DIC, saturated) ....: 5209.46
## Effective number of parameters .....................: 1753.30
## 
## Watanabe-Akaike information criterion (WAIC) ...: 9983.12
## Effective number of parameters .................: 1387.74
## 
## Marginal log-Likelihood:  -4165.30 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 21.4, Running = 4.87, Post = 0.472, Total = 26.8 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -0.134 0.026     -0.185   -0.134     -0.083 -0.134   0
## vandix_z       0.209 0.032      0.146    0.209      0.272  0.209   0
## ln_roads_km_c  1.071 0.035      1.002    1.071      1.140  1.071   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.621 0.047      0.532    0.620      0.715 0.619
## Phi for ui       0.934 0.025      0.876    0.938      0.974 0.945
## 
## Deviance Information Criterion (DIC) ...............: 9035.59
## Deviance Information Criterion (DIC, saturated) ....: 4481.80
## Effective number of parameters .....................: 1133.21
## 
## Watanabe-Akaike information criterion (WAIC) ...: 9017.56
## Effective number of parameters .................: 857.85
## 
## Marginal log-Likelihood:  -3787.50 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 20.8, Running = 5.16, Post = 0.744, Total = 26.7 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -0.291 0.031     -0.352   -0.291     -0.231
## vandix_z                       0.180 0.032      0.118    0.180      0.243
## ln_roads_km_c                  0.843 0.039      0.766    0.843      0.920
## roads_prop_highway_arterial_z  0.302 0.024      0.256    0.302      0.349
## ale_index_z                    0.041 0.045     -0.047    0.041      0.130
## canbics_index_z                0.092 0.048     -0.001    0.092      0.185
## population_100_c               0.022 0.003      0.016    0.022      0.028
##                                 mode kld
## (Intercept)                   -0.291   0
## vandix_z                       0.180   0
## ln_roads_km_c                  0.843   0
## roads_prop_highway_arterial_z  0.302   0
## ale_index_z                    0.041   0
## canbics_index_z                0.092   0
## population_100_c               0.022   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.820 0.070      0.688    0.817      0.963 0.815
## Phi for ui       0.871 0.037      0.788    0.875      0.934 0.882
## 
## Deviance Information Criterion (DIC) ...............: 8931.11
## Deviance Information Criterion (DIC, saturated) ....: 4377.32
## Effective number of parameters .....................: 1047.28
## 
## Watanabe-Akaike information criterion (WAIC) ...: 8896.67
## Effective number of parameters .................: 790.31
## 
## Marginal log-Likelihood:  -3707.54 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

van_models_3 <- cma_models(vancouver_sp@data,"Vancouver-Squamish","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
van_pedestrian <- clean_fixed_effects(van_models_3$fixed_effects)

map(van_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.176, Running = 1.08, Post = 0.165, Total = 1.42 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.020 0.031     -0.082   -0.019      0.041 -0.019   0
## vandix_z     0.358 0.029      0.302    0.358      0.415  0.358   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean   sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.716 0.03      0.659    0.715      0.776 0.714
## 
## Deviance Information Criterion (DIC) ...............: 12538.87
## Deviance Information Criterion (DIC, saturated) ....: 6593.34
## Effective number of parameters .....................: 2530.98
## 
## Watanabe-Akaike information criterion (WAIC) ...: 13203.40
## Effective number of parameters .................: 2158.93
## 
## Marginal log-Likelihood:  -6752.38 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 21, Running = 4.35, Post = 0.458, Total = 25.8 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.034 0.027     -0.088   -0.034      0.019 -0.034   0
## vandix_z     0.249 0.036      0.178    0.249      0.320  0.249   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant mode
## Precision for ui 0.493 0.035      0.428    0.492      0.564 0.49
## Phi for ui       0.666 0.044      0.576    0.667      0.748 0.67
## 
## Deviance Information Criterion (DIC) ...............: 11937.29
## Deviance Information Criterion (DIC, saturated) ....: 5991.71
## Effective number of parameters .....................: 2207.79
## 
## Watanabe-Akaike information criterion (WAIC) ...: 12268.59
## Effective number of parameters .................: 1753.57
## 
## Marginal log-Likelihood:  -5477.92 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 21.5, Running = 4.73, Post = 0.494, Total = 26.7 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   0.319 0.022      0.275    0.319      0.363 0.319   0
## vandix_z      0.289 0.032      0.227    0.289      0.352 0.289   0
## ln_roads_km_c 0.995 0.034      0.928    0.995      1.063 0.995   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.448 0.027      0.395    0.447      0.503 0.447
## Phi for ui       0.951 0.018      0.908    0.953      0.979 0.958
## 
## Deviance Information Criterion (DIC) ...............: 11177.21
## Deviance Information Criterion (DIC, saturated) ....: 5231.62
## Effective number of parameters .....................: 1631.93
## 
## Watanabe-Akaike information criterion (WAIC) ...: 11152.83
## Effective number of parameters .................: 1186.54
## 
## Marginal log-Likelihood:  -5146.55 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 22.3, Running = 5.15, Post = 0.561, Total = 28 
## Fixed effects:
##                                mean    sd 0.025quant 0.5quant 0.975quant  mode
## (Intercept)                   0.114 0.028      0.060    0.115      0.168 0.115
## vandix_z                      0.257 0.031      0.197    0.256      0.317 0.256
## ln_roads_km_c                 0.715 0.039      0.639    0.715      0.791 0.715
## roads_prop_highway_arterial_z 0.396 0.022      0.353    0.396      0.440 0.396
## ale_index_z                   0.232 0.046      0.142    0.232      0.323 0.232
## canbics_index_z               0.041 0.047     -0.051    0.041      0.134 0.041
## population_100_c              0.027 0.003      0.021    0.027      0.034 0.027
##                               kld
## (Intercept)                     0
## vandix_z                        0
## ln_roads_km_c                   0
## roads_prop_highway_arterial_z   0
## ale_index_z                     0
## canbics_index_z                 0
## population_100_c                0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.707 0.058      0.598    0.706      0.827 0.704
## Phi for ui       0.853 0.039      0.767    0.856      0.918 0.863
## 
## Deviance Information Criterion (DIC) ...............: 11048.29
## Deviance Information Criterion (DIC, saturated) ....: 5102.70
## Effective number of parameters .....................: 1481.64
## 
## Watanabe-Akaike information criterion (WAIC) ...: 10986.37
## Effective number of parameters .................: 1070.35
## 
## Marginal log-Likelihood:  -4957.32 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
van_results <- bind_rows(van_all %>% mutate(Region = "Vancouver-Squamish",Outcome = "All Injury Claims"),
                         van_cyclist %>% mutate(Region = "Vancouver-Squamish",Outcome = "Cyclist Injury Claims"),
                         van_pedestrian %>% mutate(Region = "Vancouver-Squamish",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

Victoria

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

Victoria

n_claims

579

67,182.0

116.0

176.2

0.0

1,665.0

0

1

0.2

n_casualty_claims

12,338.0

21.3

34.3

0.0

305.0

0

24

4.1

n_cyclist_claims

1,471.0

2.5

4.4

0.0

53.0

0

194

33.5

n_cyclist_casualty_claims

1,027.0

1.8

3.2

0.0

33.0

0

251

43.4

n_pedestrian_claims

896.0

1.5

3.4

0.0

49.0

0

280

48.4

n_pedestrian_casualty_claims

715.0

1.2

2.5

0.0

37.0

0

302

52.2

population

397,237.0

686.1

431.4

0.0

4,739.0

0

1

0.2

total_roads_km

3,261.2

5.6

5.6

0.5

48.0

0

0

0.0

roads_prop_highway_arterial

67.1

0.1

0.1

0.0

0.7

0

238

41.1

no_highschool_prevalance

66.7

0.1

0.1

0.0

0.4

28

0

0.0

unemployment_rate

3,099.4

5.6

3.9

0.0

30.0

28

78

13.5

hh_avg_income

41,608,895.0

77,340.0

26,930.8

26,088.0

233,035.0

41

0

0.0

participation_rate

35,068.6

63.6

11.1

18.6

92.7

28

0

0.0

university_degree_prevalance

329.1

0.6

0.1

0.3

0.9

28

0

0.0

lone_parent_fam_prevalence

84.0

0.2

0.1

0.0

0.6

30

5

0.9

home_owner_prevalence

360.4

0.7

0.2

0.0

1.0

28

3

0.5

vandix

-130.2

-0.2

0.5

-1.5

3.0

43

0

0.0

ale_index

335.8

0.6

1.8

-2.1

7.1

26

2

0.3

canbics_index

1,170.3

2.1

1.7

0.0

8.2

26

69

11.9

Maps

claims <- ggplot() + 
  geom_sf(data = victoria_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = victoria_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = victoria_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

victoria_sp <- as(victoria_sf, "Spatial")
victoria_sp$ui <- 1:nrow(victoria_sp@data)

coords <- coordinates(victoria_sp)
victoria_nb <- poly2nb(victoria_sp, queen = TRUE)

victoria_nb
## Neighbour list object:
## Number of regions: 579 
## Number of nonzero links: 3458 
## Percentage nonzero weights: 1.031497 
## Average number of links: 5.972366
#assign nearest neighbour for no links

# victoria_nb <- assign_nearest_neighbors(victoria_nb,victoria_sp)

plot(victoria_sp, border = grey(0.5))
plot(victoria_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(victoria_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(victoria_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  victoria_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 16.267, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.3909113982     -0.0017301038      0.0005825849
cyc_cc_mi <- moran.test(victoria_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  victoria_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 13.616, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.3250899021     -0.0017301038      0.0005761224
pd_cc_mi <- moran.test(victoria_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  victoria_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 15.398, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.3525248862     -0.0017301038      0.0005292953

BYM2 Models

nb2INLA("victoria.adj", victoria_nb)
g <- inla.read.graph(filename = "victoria.adj")


# Model Set 1: Total Casualty Claim Crashes

victoria_models_1 <- cma_models(victoria_sp@data, "Victoria", "n_casualty_claims", "vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
victoria_all <- clean_fixed_effects(victoria_models_1$fixed_effects)

map(victoria_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.231, Running = 0.357, Post = 0.0794, Total = 0.668 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 2.448 0.057      2.336    2.449      2.559 2.449   0
## vandix_z    0.464 0.067      0.334    0.464      0.595 0.464   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.698 0.049      0.607    0.697      0.798 0.694
## 
## Deviance Information Criterion (DIC) ...............: 3529.60
## Deviance Information Criterion (DIC, saturated) ....: 1183.69
## Effective number of parameters .....................: 536.54
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3539.96
## Effective number of parameters .................: 376.57
## 
## Marginal log-Likelihood:  -2312.02 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.2, Running = 0.861, Post = 0.255, Total = 16.3 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 2.351 0.036      2.281    2.351      2.421 2.351   0
## vandix_z    0.191 0.065      0.064    0.191      0.320 0.191   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.472 0.053      0.373     0.47      0.582 0.469
## Phi for ui       0.861 0.058      0.727     0.87      0.950 0.887
## 
## Deviance Information Criterion (DIC) ...............: 3472.56
## Deviance Information Criterion (DIC, saturated) ....: 1126.64
## Effective number of parameters .....................: 508.73
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3442.98
## Effective number of parameters .................: 334.63
## 
## Marginal log-Likelihood:  -1976.94 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.3, Running = 0.845, Post = 0.185, Total = 16.4 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   2.373 0.026      2.322    2.373      2.423 2.373   0
## vandix_z      0.315 0.053      0.212    0.315      0.419 0.315   0
## ln_roads_km_c 1.224 0.073      1.081    1.224      1.367 1.224   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.606 0.048      0.516    0.605      0.704 0.604
## Phi for ui       0.982 0.018      0.934    0.987      0.999 0.996
## 
## Deviance Information Criterion (DIC) ...............: 3403.14
## Deviance Information Criterion (DIC, saturated) ....: 1057.23
## Effective number of parameters .....................: 465.40
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3336.34
## Effective number of parameters .................: 285.26
## 
## Marginal log-Likelihood:  -1866.21 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15.4, Running = 1.02, Post = 0.204, Total = 16.6 
## Fixed effects:
##                                mean    sd 0.025quant 0.5quant 0.975quant  mode
## (Intercept)                   2.535 0.046      2.444    2.535      2.624 2.535
## vandix_z                      0.193 0.050      0.095    0.193      0.291 0.193
## ln_roads_km_c                 0.992 0.080      0.835    0.992      1.150 0.992
## roads_prop_highway_arterial_z 0.468 0.049      0.373    0.468      0.564 0.468
## ale_index_z                   0.433 0.167      0.105    0.433      0.761 0.433
## canbics_index_z               0.370 0.156      0.064    0.371      0.676 0.371
## population_100_c              0.014 0.009     -0.002    0.014      0.031 0.014
##                               kld
## (Intercept)                     0
## vandix_z                        0
## ln_roads_km_c                   0
## roads_prop_highway_arterial_z   0
## ale_index_z                     0
## canbics_index_z                 0
## population_100_c                0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.816 0.087      0.650    0.814      0.992 0.817
## Phi for ui       0.943 0.042      0.833    0.954      0.992 0.977
## 
## Deviance Information Criterion (DIC) ...............: 3399.35
## Deviance Information Criterion (DIC, saturated) ....: 1053.43
## Effective number of parameters .....................: 452.83
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3339.90
## Effective number of parameters .................: 282.83
## 
## Marginal log-Likelihood:  -1837.06 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

victoria_models_2 <- cma_models(victoria_sp@data,"Victoria","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
victoria_cyclist <- clean_fixed_effects(victoria_models_2$fixed_effects)

map(victoria_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.202, Running = 0.325, Post = 0.085, Total = 0.613 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.089 0.081     -0.252   -0.087      0.065 -0.087   0
## vandix_z     0.283 0.082      0.123    0.283      0.445  0.283   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.719 0.079      0.577    0.715      0.884 0.707
## 
## Deviance Information Criterion (DIC) ...............: 1844.26
## Deviance Information Criterion (DIC, saturated) ....: 959.95
## Effective number of parameters .....................: 347.61
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1886.31
## Effective number of parameters .................: 271.71
## 
## Marginal log-Likelihood:  -1041.17 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.5, Running = 0.839, Post = 0.178, Total = 16.5 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.132 0.070     -0.274   -0.131      0.003 -0.132   0
## vandix_z     0.142 0.086     -0.026    0.142      0.311  0.142   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.663 0.095      0.495    0.657      0.867 0.645
## Phi for ui       0.625 0.102      0.414    0.630      0.808 0.640
## 
## Deviance Information Criterion (DIC) ...............: 1756.80
## Deviance Information Criterion (DIC, saturated) ....: 872.49
## Effective number of parameters .....................: 289.31
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1758.54
## Effective number of parameters .................: 211.38
## 
## Marginal log-Likelihood:  -738.92 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.4, Running = 0.847, Post = 0.158, Total = 16.4 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -0.133 0.065     -0.263   -0.133     -0.007 -0.133   0
## vandix_z       0.239 0.080      0.082    0.239      0.396  0.239   0
## ln_roads_km_c  1.091 0.115      0.866    1.091      1.318  1.091   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.635 0.094      0.465    0.630      0.835 0.622
## Phi for ui       0.901 0.064      0.740    0.916      0.983 0.950
## 
## Deviance Information Criterion (DIC) ...............: 1693.82
## Deviance Information Criterion (DIC, saturated) ....: 809.50
## Effective number of parameters .....................: 240.25
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1685.78
## Effective number of parameters .................: 174.70
## 
## Marginal log-Likelihood:  -702.76 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15.7, Running = 0.999, Post = 0.226, Total = 17 
## Fixed effects:
##                                mean    sd 0.025quant 0.5quant 0.975quant  mode
## (Intercept)                   0.053 0.080     -0.106    0.054      0.207 0.054
## vandix_z                      0.111 0.080     -0.046    0.111      0.269 0.111
## ln_roads_km_c                 0.882 0.129      0.629    0.882      1.135 0.882
## roads_prop_highway_arterial_z 0.309 0.073      0.167    0.309      0.452 0.309
## ale_index_z                   0.400 0.221     -0.033    0.400      0.835 0.400
## canbics_index_z               0.604 0.212      0.187    0.604      1.021 0.604
## population_100_c              0.030 0.014      0.004    0.030      0.057 0.030
##                               kld
## (Intercept)                     0
## vandix_z                        0
## ln_roads_km_c                   0
## roads_prop_highway_arterial_z   0
## ale_index_z                     0
## canbics_index_z                 0
## population_100_c                0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.845 0.140      0.598    0.835      1.146 0.820
## Phi for ui       0.821 0.093      0.601    0.837      0.955 0.876
## 
## Deviance Information Criterion (DIC) ...............: 1686.20
## Deviance Information Criterion (DIC, saturated) ....: 801.88
## Effective number of parameters .....................: 225.70
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1680.27
## Effective number of parameters .................: 167.09
## 
## Marginal log-Likelihood:  -703.74 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

victoria_models_3 <- cma_models(victoria_sp@data,"Victoria","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
victoria_pedestrian <- clean_fixed_effects(victoria_models_3$fixed_effects)

map(victoria_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.188, Running = 0.343, Post = 0.167, Total = 0.698 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.400 0.087     -0.576   -0.398     -0.235 -0.398   0
## vandix_z     0.476 0.083      0.314    0.476      0.641  0.476   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.778 0.095      0.608    0.772      0.981 0.761
## 
## Deviance Information Criterion (DIC) ...............: 1562.25
## Deviance Information Criterion (DIC, saturated) ....: 852.75
## Effective number of parameters .....................: 289.25
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1578.17
## Effective number of parameters .................: 217.49
## 
## Marginal log-Likelihood:  -869.32 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.3, Running = 0.822, Post = 0.18, Total = 16.3 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.428 0.074     -0.578   -0.427     -0.284 -0.427   0
## vandix_z     0.343 0.085      0.177    0.343      0.509  0.343   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.609 0.098      0.437    0.603      0.821 0.591
## Phi for ui       0.794 0.096      0.571    0.808      0.939 0.842
## 
## Deviance Information Criterion (DIC) ...............: 1480.46
## Deviance Information Criterion (DIC, saturated) ....: 770.97
## Effective number of parameters .....................: 228.15
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1477.13
## Effective number of parameters .................: 167.72
## 
## Marginal log-Likelihood:  -578.10 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.5, Running = 0.866, Post = 0.189, Total = 16.5 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -0.417 0.071     -0.560   -0.417     -0.279 -0.417   0
## vandix_z       0.442 0.081      0.282    0.442      0.602  0.442   0
## ln_roads_km_c  0.847 0.118      0.617    0.847      1.080  0.847   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.587 0.087      0.433    0.582      0.775 0.571
## Phi for ui       0.951 0.045      0.828    0.965      0.996 0.988
## 
## Deviance Information Criterion (DIC) ...............: 1439.74
## Deviance Information Criterion (DIC, saturated) ....: 730.24
## Effective number of parameters .....................: 198.88
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1430.00
## Effective number of parameters .................: 144.74
## 
## Marginal log-Likelihood:  -559.20 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15.6, Running = 0.938, Post = 0.207, Total = 16.8 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -0.297 0.090     -0.477   -0.296     -0.125
## vandix_z                       0.311 0.082      0.150    0.311      0.471
## ln_roads_km_c                  0.571 0.135      0.306    0.571      0.837
## roads_prop_highway_arterial_z  0.386 0.079      0.232    0.386      0.542
## ale_index_z                    0.543 0.236      0.083    0.542      1.011
## canbics_index_z                0.343 0.235     -0.120    0.343      0.802
## population_100_c               0.036 0.014      0.009    0.036      0.064
##                                 mode kld
## (Intercept)                   -0.296   0
## vandix_z                       0.311   0
## ln_roads_km_c                  0.571   0
## roads_prop_highway_arterial_z  0.386   0
## ale_index_z                    0.542   0
## canbics_index_z                0.343   0
## population_100_c               0.036   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.724 0.119      0.515    0.716      0.981 0.702
## Phi for ui       0.924 0.066      0.745    0.944      0.993 0.980
## 
## Deviance Information Criterion (DIC) ...............: 1426.57
## Deviance Information Criterion (DIC, saturated) ....: 717.08
## Effective number of parameters .....................: 184.56
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1418.88
## Effective number of parameters .................: 136.76
## 
## Marginal log-Likelihood:  -560.52 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
victoria_results <- bind_rows(victoria_all %>% mutate(Region = "Victoria",Outcome = "All Injury Claims"),
                         victoria_cyclist %>% mutate(Region = "Victoria",Outcome = "Cyclist Injury Claims"),
                         victoria_pedestrian %>% mutate(Region = "Victoria",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

Central Island - Powell River

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

Central Island-Powell River

n_claims

601

62,992.0

104.8

165.5

0.0

1,934.0

0

7

1.2

n_casualty_claims

10,762.0

17.9

28.4

0.0

203.0

0

37

6.2

n_cyclist_claims

475.0

0.8

1.5

0.0

14.0

0

355

59.1

n_cyclist_casualty_claims

271.0

0.5

0.9

0.0

10.0

0

425

70.7

n_pedestrian_claims

673.0

1.1

2.4

0.0

23.0

0

351

58.4

n_pedestrian_casualty_claims

547.0

0.9

2.0

0.0

18.0

0

377

62.7

population

357,163.0

594.3

301.0

0.0

2,466.0

0

5

0.8

total_roads_km

5,652.1

9.4

9.9

0.1

86.5

0

0

0.0

roads_prop_highway_arterial

78.2

0.1

0.2

0.0

0.8

0

262

43.6

no_highschool_prevalance

101.2

0.2

0.1

0.0

0.6

28

1

0.2

unemployment_rate

4,784.2

8.3

5.2

0.0

40.0

28

43

7.2

hh_avg_income

36,682,051.0

65,738.4

17,197.1

29,925.0

211,531.0

43

0

0.0

participation_rate

32,393.0

56.5

11.0

12.0

86.4

28

0

0.0

university_degree_prevalance

300.2

0.5

0.1

0.2

0.8

28

0

0.0

lone_parent_fam_prevalence

95.7

0.2

0.1

0.0

0.6

28

3

0.5

home_owner_prevalence

426.2

0.7

0.2

0.0

1.0

28

1

0.2

vandix

111.8

0.2

0.7

-1.1

4.0

43

0

0.0

ale_index

-590.4

-1.1

0.7

-2.1

1.5

47

0

0.0

canbics_index

326.8

0.6

0.9

0.0

4.2

45

241

40.1

Maps

claims <- ggplot() + 
  geom_sf(data = nanaimo_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = nanaimo_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = nanaimo_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

nanaimo_sp <- as(nanaimo_sf, "Spatial")
nanaimo_sp$ui <- 1:nrow(nanaimo_sp@data)

coords <- coordinates(nanaimo_sp)
nanaimo_nb <- poly2nb(nanaimo_sp, queen = TRUE)
## Warning in poly2nb(nanaimo_sp, queen = TRUE): neighbour object has 5 sub-graphs;
## if this sub-graph count seems unexpected, try increasing the snap argument.
nanaimo_nb
## Neighbour list object:
## Number of regions: 601 
## Number of nonzero links: 3312 
## Percentage nonzero weights: 0.916941 
## Average number of links: 5.510815 
## 5 disjoint connected subgraphs
#assign nearest neighbour for no links

nanaimo_nb <- assign_nearest_neighbors(nanaimo_nb,nanaimo_sp)

plot(nanaimo_sp, border = grey(0.5))
plot(nanaimo_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(nanaimo_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(nanaimo_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  nanaimo_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 12.045, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.3052806361     -0.0016666667      0.0006494328
cyc_cc_mi <- moran.test(nanaimo_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  nanaimo_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 6.6644, p-value = 1.328e-11
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.1663894111     -0.0016666667      0.0006358885
pd_cc_mi <- moran.test(nanaimo_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  nanaimo_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 8.5689, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.2149591347     -0.0016666667      0.0006391025

BYM2 Models

nb2INLA("nanaimo.adj", nanaimo_nb)
g <- inla.read.graph(filename = "nanaimo.adj")


# Model Set 1: Total Casualty Claim Crashes

nanaimo_models_1 <- cma_models(nanaimo_sp@data, "Central Island-Powell River", "n_casualty_claims", "vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
nanaimo_all <- clean_fixed_effects(nanaimo_models_1$fixed_effects)

map(nanaimo_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.23, Running = 0.35, Post = 0.0738, Total = 0.654 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 1.969 0.058      1.854    1.969      2.083 1.969   0
## vandix_z    0.326 0.055      0.218    0.326      0.434 0.326   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant mode
## Precision for ui 0.633 0.044       0.55    0.632      0.723 0.63
## 
## Deviance Information Criterion (DIC) ...............: 3525.72
## Deviance Information Criterion (DIC, saturated) ....: 1233.27
## Effective number of parameters .....................: 553.20
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3560.31
## Effective number of parameters .................: 402.22
## 
## Marginal log-Likelihood:  -2298.87 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 16.2, Running = 0.883, Post = 0.202, Total = 17.3 
## Fixed effects:
##             mean    sd 0.025quant 0.5quant 0.975quant mode kld
## (Intercept) 1.98 0.051      1.878     1.98      2.079 1.98   0
## vandix_z    0.29 0.059      0.173     0.29      0.407 0.29   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.474 0.067      0.357    0.469      0.622 0.457
## Phi for ui       0.478 0.106      0.271    0.478      0.684 0.482
## 
## Deviance Information Criterion (DIC) ...............: 3515.76
## Deviance Information Criterion (DIC, saturated) ....: 1223.31
## Effective number of parameters .....................: 547.76
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3543.60
## Effective number of parameters .................: 394.79
## 
## Marginal log-Likelihood:  -2179.69 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 16.5, Running = 0.995, Post = 0.167, Total = 17.6 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   1.437 0.061      1.317    1.438      1.556 1.438   0
## vandix_z      0.418 0.053      0.315    0.417      0.521 0.417   0
## ln_roads_km_c 0.971 0.070      0.835    0.971      1.109 0.971   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.484 0.060      0.377    0.480      0.615 0.472
## Phi for ui       0.684 0.066      0.544    0.688      0.801 0.698
## 
## Deviance Information Criterion (DIC) ...............: 3456.63
## Deviance Information Criterion (DIC, saturated) ....: 1164.18
## Effective number of parameters .....................: 520.34
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3444.08
## Effective number of parameters .................: 353.05
## 
## Marginal log-Likelihood:  -2095.62 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 16.5, Running = 0.999, Post = 0.196, Total = 17.7 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                    2.114 0.118      1.881    2.114      2.345
## vandix_z                       0.313 0.045      0.225    0.313      0.402
## ln_roads_km_c                  0.619 0.073      0.476    0.619      0.763
## roads_prop_highway_arterial_z  0.662 0.047      0.569    0.661      0.755
## ale_index_z                    1.434 0.244      0.957    1.434      1.913
## canbics_index_z               -0.657 0.228     -1.106   -0.657     -0.211
## population_100_c               0.063 0.013      0.037    0.063      0.089
##                                 mode kld
## (Intercept)                    2.114   0
## vandix_z                       0.313   0
## ln_roads_km_c                  0.619   0
## roads_prop_highway_arterial_z  0.661   0
## ale_index_z                    1.434   0
## canbics_index_z               -0.657   0
## population_100_c               0.063   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.768 0.096      0.596    0.762      0.973 0.751
## Phi for ui       0.648 0.070      0.503    0.651      0.775 0.658
## 
## Deviance Information Criterion (DIC) ...............: 3426.18
## Deviance Information Criterion (DIC, saturated) ....: 1133.72
## Effective number of parameters .....................: 490.47
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3391.55
## Effective number of parameters .................: 322.45
## 
## Marginal log-Likelihood:  -2020.82 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

nanaimo_models_2 <- cma_models(nanaimo_sp@data,"Central Island-Powell River","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
nanaimo_cyclist <- clean_fixed_effects(nanaimo_models_2$fixed_effects)

map(nanaimo_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.19, Running = 0.344, Post = 0.11, Total = 0.643 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.395 0.115     -1.630   -1.392     -1.177 -1.392   0
## vandix_z     0.280 0.072      0.139    0.280      0.421  0.280   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                  mean    sd 0.025quant 0.5quant 0.975quant mode
## Precision for ui 1.19 0.238      0.806     1.16       1.73 1.11
## 
## Deviance Information Criterion (DIC) ...............: 1019.00
## Deviance Information Criterion (DIC, saturated) ....: 621.37
## Effective number of parameters .....................: 146.46
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1013.31
## Effective number of parameters .................: 110.95
## 
## Marginal log-Likelihood:  -548.78 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 16.4, Running = 0.894, Post = 0.245, Total = 17.6 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.399 0.109     -1.622   -1.396     -1.190 -1.396   0
## vandix_z     0.314 0.074      0.169    0.314      0.459  0.314   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.077 0.242      0.689    1.047      1.638 0.985
## Phi for ui       0.311 0.144      0.080    0.295      0.624 0.249
## 
## Deviance Information Criterion (DIC) ...............: 1008.22
## Deviance Information Criterion (DIC, saturated) ....: 610.59
## Effective number of parameters .....................: 136.69
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1004.54
## Effective number of parameters .................: 105.65
## 
## Marginal log-Likelihood:  -437.96 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 16.2, Running = 0.972, Post = 0.176, Total = 17.3 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -1.683 0.138     -1.961   -1.681     -1.419 -1.681   0
## vandix_z       0.374 0.075      0.227    0.374      0.521  0.374   0
## ln_roads_km_c  0.475 0.116      0.249    0.474      0.705  0.474   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.948 0.236      0.574    0.918      1.497 0.859
## Phi for ui       0.532 0.154      0.229    0.536      0.812 0.552
## 
## Deviance Information Criterion (DIC) ...............: 991.67
## Deviance Information Criterion (DIC, saturated) ....: 594.04
## Effective number of parameters .....................: 126.50
## 
## Watanabe-Akaike information criterion (WAIC) ...: 991.03
## Effective number of parameters .................: 100.43
## 
## Marginal log-Likelihood:  -435.16 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 16.6, Running = 1.02, Post = 0.222, Total = 17.8 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -1.050 0.207     -1.465   -1.047     -0.651
## vandix_z                       0.334 0.076      0.186    0.334      0.482
## ln_roads_km_c                  0.277 0.138      0.008    0.276      0.548
## roads_prop_highway_arterial_z  0.426 0.081      0.267    0.426      0.587
## ale_index_z                    1.184 0.409      0.385    1.182      1.991
## canbics_index_z               -0.239 0.365     -0.959   -0.237      0.475
## population_100_c               0.056 0.024      0.010    0.056      0.103
##                                 mode kld
## (Intercept)                   -1.047   0
## vandix_z                       0.334   0
## ln_roads_km_c                  0.276   0
## roads_prop_highway_arterial_z  0.426   0
## ale_index_z                    1.182   0
## canbics_index_z               -0.237   0
## population_100_c               0.056   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.218 0.321      0.719    1.174      1.974 1.086
## Phi for ui       0.466 0.156      0.174    0.464      0.765 0.469
## 
## Deviance Information Criterion (DIC) ...............: 968.35
## Deviance Information Criterion (DIC, saturated) ....: 570.71
## Effective number of parameters .....................: 113.36
## 
## Watanabe-Akaike information criterion (WAIC) ...: 968.76
## Effective number of parameters .................: 91.87
## 
## Marginal log-Likelihood:  -436.30 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

nanaimo_models_3 <- cma_models(nanaimo_sp@data,"Central Island-Powell River","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
nanaimo_pedestrian <- clean_fixed_effects(nanaimo_models_3$fixed_effects)

map(nanaimo_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.199, Running = 0.346, Post = 0.0696, Total = 0.614 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.243 0.123     -1.497   -1.239     -1.013 -1.239   0
## vandix_z     0.517 0.075      0.372    0.517      0.665  0.517   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.631 0.084      0.483    0.626       0.81 0.615
## 
## Deviance Information Criterion (DIC) ...............: 1367.05
## Deviance Information Criterion (DIC, saturated) ....: 801.25
## Effective number of parameters .....................: 285.30
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1400.20
## Effective number of parameters .................: 221.21
## 
## Marginal log-Likelihood:  -757.92 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 16.4, Running = 0.877, Post = 0.191, Total = 17.5 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.213 0.115     -1.453   -1.209     -0.999 -1.209   0
## vandix_z     0.524 0.077      0.375    0.524      0.676  0.524   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.607 0.099      0.441    0.597      0.831 0.574
## Phi for ui       0.206 0.125      0.032    0.181      0.502 0.107
## 
## Deviance Information Criterion (DIC) ...............: 1351.33
## Deviance Information Criterion (DIC, saturated) ....: 785.53
## Effective number of parameters .....................: 272.72
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1371.85
## Effective number of parameters .................: 206.15
## 
## Marginal log-Likelihood:  -651.06 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 16.7, Running = 0.926, Post = 0.184, Total = 17.8 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -1.540 0.139     -1.821   -1.538     -1.275 -1.538   0
## vandix_z       0.578 0.078      0.425    0.578      0.733  0.578   0
## ln_roads_km_c  0.614 0.130      0.361    0.613      0.870  0.613   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.470 0.104      0.302    0.458      0.709 0.434
## Phi for ui       0.578 0.143      0.281    0.587      0.827 0.620
## 
## Deviance Information Criterion (DIC) ...............: 1312.28
## Deviance Information Criterion (DIC, saturated) ....: 746.48
## Effective number of parameters .....................: 240.68
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1324.29
## Effective number of parameters .................: 181.98
## 
## Marginal log-Likelihood:  -645.55 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 16.5, Running = 1.02, Post = 0.236, Total = 17.8 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -0.644 0.206     -1.056   -0.641     -0.249
## vandix_z                       0.494 0.074      0.349    0.494      0.639
## ln_roads_km_c                  0.308 0.139      0.037    0.308      0.581
## roads_prop_highway_arterial_z  0.549 0.081      0.391    0.549      0.710
## ale_index_z                    2.409 0.391      1.647    2.407      3.181
## canbics_index_z               -1.066 0.349     -1.757   -1.064     -0.387
## population_100_c               0.112 0.023      0.068    0.112      0.157
##                                 mode kld
## (Intercept)                   -0.641   0
## vandix_z                       0.494   0
## ln_roads_km_c                  0.308   0
## roads_prop_highway_arterial_z  0.549   0
## ale_index_z                    2.407   0
## canbics_index_z               -1.064   0
## population_100_c               0.112   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.765 0.161      0.504    0.746      1.136 0.707
## Phi for ui       0.423 0.150      0.150    0.419      0.718 0.420
## 
## Deviance Information Criterion (DIC) ...............: 1262.65
## Deviance Information Criterion (DIC, saturated) ....: 696.85
## Effective number of parameters .....................: 201.64
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1262.54
## Effective number of parameters .................: 150.54
## 
## Marginal log-Likelihood:  -621.15 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
nanaimo_results <- bind_rows(nanaimo_all %>% mutate(Region = "Central Island-Powell River",Outcome = "All Injury Claims"),
                         nanaimo_cyclist %>% mutate(Region = "Central Island-Powell River",Outcome = "Cyclist Injury Claims"),
                         nanaimo_pedestrian %>% mutate(Region = "Central Island-Powell River",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

Okanagan

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

Okanagan

n_claims

464

70,024.0

150.9

326.1

0.0

4,324.0

0

8

1.7

n_casualty_claims

13,236.0

28.5

66.7

0.0

938.0

0

36

7.8

n_cyclist_claims

761.0

1.6

3.8

0.0

38.0

0

250

53.9

n_cyclist_casualty_claims

485.0

1.0

2.3

0.0

23.0

0

284

61.2

n_pedestrian_claims

696.0

1.5

3.9

0.0

41.0

0

257

55.4

n_pedestrian_casualty_claims

564.0

1.2

3.2

0.0

35.0

0

272

58.6

population

336,628.0

725.5

488.3

0.0

4,622.0

0

8

1.7

total_roads_km

4,759.1

10.3

13.6

0.0

139.3

0

0

0.0

roads_prop_highway_arterial

60.1

0.1

0.2

0.0

1.0

0

199

42.9

no_highschool_prevalance

62.0

0.2

0.1

0.0

0.4

86

4

0.9

unemployment_rate

2,933.5

7.8

4.7

0.0

33.3

86

28

6.0

hh_avg_income

26,784,003.0

72,980.9

26,808.0

26,241.0

247,493.0

97

0

0.0

participation_rate

23,166.9

61.3

12.9

9.2

91.5

86

0

0.0

university_degree_prevalance

199.0

0.5

0.1

0.3

0.8

86

0

0.0

lone_parent_fam_prevalence

59.9

0.2

0.1

0.0

0.5

86

4

0.9

home_owner_prevalence

275.1

0.7

0.2

0.0

1.3

86

0

0.0

vandix

42.6

0.1

0.6

-1.2

2.2

97

0

0.0

ale_index

-314.5

-0.8

1.0

-2.1

2.3

91

1

0.2

canbics_index

709.8

1.9

1.8

0.0

7.2

91

82

17.7

Maps

claims <- ggplot() + 
  geom_sf(data = okanagan_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = okanagan_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = okanagan_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

okanagan_sp <- as(okanagan_sf, "Spatial")
okanagan_sp$ui <- 1:nrow(okanagan_sp@data)

coords <- coordinates(okanagan_sp)
okanagan_nb <- poly2nb(okanagan_sp, queen = TRUE,snap = 1)

okanagan_nb
## Neighbour list object:
## Number of regions: 464 
## Number of nonzero links: 2720 
## Percentage nonzero weights: 1.263377 
## Average number of links: 5.862069
#assign nearest neighbour for no links

# okanagan_nb <- assign_nearest_neighbors(okanagan_nb,okanagan_sp)

plot(okanagan_sp, border = grey(0.5))
plot(okanagan_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(okanagan_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(okanagan_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  okanagan_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 14.418, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.3622147009     -0.0021598272      0.0006386753
cyc_cc_mi <- moran.test(okanagan_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  okanagan_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 14.971, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.3999237322     -0.0021598272      0.0007213349
pd_cc_mi <- moran.test(okanagan_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  okanagan_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 8.8393, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.2314383441     -0.0021598272      0.0006983917

BYM2 Models

nb2INLA("okanagan.adj", okanagan_nb)
g <- inla.read.graph(filename = "okanagan.adj")


# Model Set 1: Total Casualty Claim Crashes

okanagan_models_1 <- cma_models(okanagan_sp@data, "Okanagan", "n_casualty_claims", "vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
okanagan_all <- clean_fixed_effects(okanagan_models_1$fixed_effects)

map(okanagan_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.203, Running = 0.339, Post = 0.0737, Total = 0.616 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 2.176 0.073      2.031    2.177      2.319 2.177   0
## vandix_z    0.442 0.084      0.279    0.442      0.607 0.442   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.471 0.037      0.402     0.47      0.546 0.467
## 
## Deviance Information Criterion (DIC) ...............: 2820.09
## Deviance Information Criterion (DIC, saturated) ....: 969.14
## Effective number of parameters .....................: 439.12
## 
## Watanabe-Akaike information criterion (WAIC) ...: 2859.13
## Effective number of parameters .................: 324.59
## 
## Marginal log-Likelihood:  -1924.88 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.2, Running = 0.891, Post = 0.145, Total = 16.2 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 2.179 0.047      2.087    2.179      2.270 2.179   0
## vandix_z    0.329 0.091      0.151    0.329      0.507 0.329   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.240 0.037      0.175    0.238      0.320 0.233
## Phi for ui       0.842 0.059      0.705    0.850      0.932 0.866
## 
## Deviance Information Criterion (DIC) ...............: 2777.98
## Deviance Information Criterion (DIC, saturated) ....: 927.03
## Effective number of parameters .....................: 421.57
## 
## Watanabe-Akaike information criterion (WAIC) ...: 2779.92
## Effective number of parameters .................: 290.97
## 
## Marginal log-Likelihood:  -1781.47 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.2, Running = 0.857, Post = 0.164, Total = 16.2 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   1.597 0.052      1.493    1.597      1.699 1.597   0
## vandix_z      0.438 0.073      0.294    0.438      0.582 0.438   0
## ln_roads_km_c 1.136 0.073      0.993    1.136      1.280 1.136   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.243 0.022      0.200    0.242      0.287 0.242
## Phi for ui       0.985 0.013      0.949    0.989      0.999 0.996
## 
## Deviance Information Criterion (DIC) ...............: 2701.46
## Deviance Information Criterion (DIC, saturated) ....: 850.50
## Effective number of parameters .....................: 385.80
## 
## Watanabe-Akaike information criterion (WAIC) ...: 2649.57
## Effective number of parameters .................: 235.72
## 
## Marginal log-Likelihood:  -1686.96 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15.2, Running = 0.859, Post = 0.315, Total = 16.4 
## Fixed effects:
##                                mean    sd 0.025quant 0.5quant 0.975quant  mode
## (Intercept)                   1.990 0.084      1.823    1.990      2.154 1.990
## vandix_z                      0.336 0.064      0.210    0.336      0.462 0.336
## ln_roads_km_c                 0.949 0.076      0.800    0.949      1.098 0.949
## roads_prop_highway_arterial_z 0.599 0.054      0.492    0.599      0.706 0.599
## ale_index_z                   0.536 0.263      0.020    0.536      1.052 0.536
## canbics_index_z               0.032 0.215     -0.390    0.031      0.454 0.031
## population_100_c              0.030 0.009      0.014    0.030      0.047 0.030
##                               kld
## (Intercept)                     0
## vandix_z                        0
## ln_roads_km_c                   0
## roads_prop_highway_arterial_z   0
## ale_index_z                     0
## canbics_index_z                 0
## population_100_c                0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.341 0.037      0.271    0.340      0.415 0.342
## Phi for ui       0.979 0.020      0.927    0.985      0.998 0.995
## 
## Deviance Information Criterion (DIC) ...............: 2692.22
## Deviance Information Criterion (DIC, saturated) ....: 841.26
## Effective number of parameters .....................: 370.67
## 
## Watanabe-Akaike information criterion (WAIC) ...: 2639.76
## Effective number of parameters .................: 226.92
## 
## Marginal log-Likelihood:  -1648.95 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

okanagan_models_2 <- cma_models(okanagan_sp@data,"Okanagan","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
okanagan_cyclist <- clean_fixed_effects(okanagan_models_2$fixed_effects)

map(okanagan_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.174, Running = 0.309, Post = 0.0941, Total = 0.577 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.110 0.136     -1.392   -1.104     -0.857 -1.083   0
## vandix_z     0.665 0.103      0.467    0.664      0.870  0.664   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.591 0.086       0.44    0.585      0.776 0.574
## 
## Deviance Information Criterion (DIC) ...............: 1108.00
## Deviance Information Criterion (DIC, saturated) ....: 639.28
## Effective number of parameters .....................: 233.10
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1142.81
## Effective number of parameters .................: 184.75
## 
## Marginal log-Likelihood:  -625.00 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.3, Running = 0.691, Post = 0.152, Total = 16.1 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.104 0.110     -1.327   -1.102     -0.893 -1.102   0
## vandix_z     0.618 0.108      0.408    0.618      0.832  0.618   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.416 0.090      0.263    0.407      0.617 0.392
## Phi for ui       0.799 0.092      0.582    0.813      0.937 0.845
## 
## Deviance Information Criterion (DIC) ...............: 994.90
## Deviance Information Criterion (DIC, saturated) ....: 526.17
## Effective number of parameters .....................: 160.48
## 
## Watanabe-Akaike information criterion (WAIC) ...: 993.45
## Effective number of parameters .................: 117.58
## 
## Marginal log-Likelihood:  -488.84 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.1, Running = 0.727, Post = 0.194, Total = 16.1 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -1.493 0.139     -1.773   -1.490     -1.225 -1.491   0
## vandix_z       0.676 0.104      0.474    0.676      0.882  0.676   0
## ln_roads_km_c  0.711 0.121      0.474    0.711      0.951  0.711   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean   sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.333 0.06      0.228    0.329      0.465 0.321
## Phi for ui       0.954 0.04      0.847    0.965      0.995 0.985
## 
## Deviance Information Criterion (DIC) ...............: 964.39
## Deviance Information Criterion (DIC, saturated) ....: 495.66
## Effective number of parameters .....................: 141.22
## 
## Watanabe-Akaike information criterion (WAIC) ...: 957.61
## Effective number of parameters .................: 101.59
## 
## Marginal log-Likelihood:  -478.14 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15, Running = 0.756, Post = 0.189, Total = 16 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -0.989 0.165     -1.320   -0.987     -0.673
## vandix_z                       0.545 0.099      0.351    0.544      0.741
## ln_roads_km_c                  0.612 0.137      0.344    0.612      0.882
## roads_prop_highway_arterial_z  0.396 0.089      0.222    0.396      0.570
## ale_index_z                    0.730 0.380     -0.014    0.730      1.476
## canbics_index_z                0.361 0.292     -0.214    0.362      0.934
## population_100_c               0.036 0.015      0.008    0.036      0.065
##                                 mode kld
## (Intercept)                   -0.987   0
## vandix_z                       0.544   0
## ln_roads_km_c                  0.612   0
## roads_prop_highway_arterial_z  0.396   0
## ale_index_z                    0.730   0
## canbics_index_z                0.362   0
## population_100_c               0.036   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.424 0.080      0.286    0.417      0.601 0.405
## Phi for ui       0.962 0.037      0.862    0.974      0.997 0.992
## 
## Deviance Information Criterion (DIC) ...............: 951.85
## Deviance Information Criterion (DIC, saturated) ....: 483.12
## Effective number of parameters .....................: 124.57
## 
## Watanabe-Akaike information criterion (WAIC) ...: 945.73
## Effective number of parameters .................: 91.64
## 
## Marginal log-Likelihood:  -480.85 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

okanagan_models_3 <- cma_models(okanagan_sp@data,"Okanagan","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
okanagan_pedestrian <- clean_fixed_effects(okanagan_models_3$fixed_effects)

map(okanagan_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.214, Running = 0.312, Post = 0.086, Total = 0.612 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.064 0.131     -1.335   -1.059     -0.819 -1.059   0
## vandix_z     0.623 0.103      0.423    0.622      0.827  0.622   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant mode
## Precision for ui 0.554 0.074      0.421    0.549      0.712 0.54
## 
## Deviance Information Criterion (DIC) ...............: 1152.02
## Deviance Information Criterion (DIC, saturated) ....: 657.89
## Effective number of parameters .....................: 246.82
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1197.10
## Effective number of parameters .................: 198.98
## 
## Marginal log-Likelihood:  -650.99 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15, Running = 0.71, Post = 0.139, Total = 15.9 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.032 0.117     -1.274   -1.029     -0.813 -1.029   0
## vandix_z     0.645 0.110      0.428    0.645      0.861  0.645   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.515 0.088      0.365    0.507       0.71 0.492
## Phi for ui       0.346 0.124      0.133    0.336       0.61 0.314
## 
## Deviance Information Criterion (DIC) ...............: 1113.50
## Deviance Information Criterion (DIC, saturated) ....: 619.37
## Effective number of parameters .....................: 219.98
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1131.58
## Effective number of parameters .................: 166.72
## 
## Marginal log-Likelihood:  -555.26 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.2, Running = 0.723, Post = 0.164, Total = 16.1 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -1.428 0.138     -1.706   -1.426     -1.163 -1.426   0
## vandix_z       0.693 0.118      0.462    0.692      0.925  0.692   0
## ln_roads_km_c  0.803 0.136      0.537    0.802      1.071  0.802   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.357 0.079      0.224    0.350      0.536 0.335
## Phi for ui       0.770 0.108      0.518    0.787      0.932 0.827
## 
## Deviance Information Criterion (DIC) ...............: 1069.25
## Deviance Information Criterion (DIC, saturated) ....: 575.11
## Effective number of parameters .....................: 184.54
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1069.33
## Effective number of parameters .................: 134.51
## 
## Marginal log-Likelihood:  -543.63 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15, Running = 0.793, Post = 0.181, Total = 16 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -0.836 0.160     -1.157   -0.834     -0.530
## vandix_z                       0.532 0.111      0.314    0.532      0.750
## ln_roads_km_c                  0.634 0.150      0.339    0.634      0.930
## roads_prop_highway_arterial_z  0.574 0.088      0.403    0.574      0.748
## ale_index_z                    1.330 0.392      0.565    1.329      2.103
## canbics_index_z               -0.240 0.322     -0.875   -0.240      0.390
## population_100_c               0.049 0.016      0.018    0.049      0.080
##                                 mode kld
## (Intercept)                   -0.834   0
## vandix_z                       0.532   0
## ln_roads_km_c                  0.634   0
## roads_prop_highway_arterial_z  0.574   0
## ale_index_z                    1.329   0
## canbics_index_z               -0.240   0
## population_100_c               0.049   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.494 0.120      0.299    0.481      0.767 0.456
## Phi for ui       0.722 0.131      0.422    0.740      0.920 0.790
## 
## Deviance Information Criterion (DIC) ...............: 1039.35
## Deviance Information Criterion (DIC, saturated) ....: 545.21
## Effective number of parameters .....................: 163.80
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1034.42
## Effective number of parameters .................: 118.27
## 
## Marginal log-Likelihood:  -535.00 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
okanagan_results <- bind_rows(okanagan_all %>% mutate(Region = "Okanagan",Outcome = "All Injury Claims"),
                         okanagan_cyclist %>% mutate(Region = "Okanagan",Outcome = "Cyclist Injury Claims"),
                         okanagan_pedestrian %>% mutate(Region = "Okanagan",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

Fraser Valley

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

Fraser Valley

n_claims

472

68,269.0

144.6

279.9

0.0

2,538.0

0

4

0.8

n_casualty_claims

15,730.0

33.3

65.2

0.0

556.0

0

17

3.6

n_cyclist_claims

581.0

1.2

2.4

0.0

21.0

0

248

52.5

n_cyclist_casualty_claims

360.0

0.8

1.6

0.0

12.0

0

302

64.0

n_pedestrian_claims

894.0

1.9

3.7

0.0

32.0

0

205

43.4

n_pedestrian_casualty_claims

725.0

1.5

3.0

0.0

25.0

0

225

47.7

population

309,493.0

655.7

341.8

0.0

2,550.0

0

4

0.8

total_roads_km

3,678.9

7.8

9.6

0.1

81.8

0

0

0.0

roads_prop_highway_arterial

40.5

0.1

0.1

0.0

0.7

0

281

59.5

no_highschool_prevalance

82.9

0.2

0.1

0.1

0.5

88

0

0.0

unemployment_rate

2,706.8

7.0

5.1

0.0

30.0

88

45

9.5

hh_avg_income

27,748,698.0

75,404.1

21,091.5

24,502.0

161,236.0

104

0

0.0

participation_rate

24,427.3

63.6

11.6

12.7

82.2

88

0

0.0

university_degree_prevalance

170.5

0.4

0.1

0.1

0.7

88

0

0.0

lone_parent_fam_prevalence

63.8

0.2

0.1

0.0

1.0

87

3

0.6

home_owner_prevalence

284.5

0.7

0.2

0.0

1.0

88

1

0.2

vandix

112.4

0.3

0.6

-0.9

2.0

104

0

0.0

ale_index

-89.0

-0.2

1.7

-2.1

6.7

101

1

0.2

canbics_index

514.5

1.4

1.3

0.0

4.9

101

81

17.2

Maps

claims <- ggplot() + 
  geom_sf(data = fraser_valley_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = fraser_valley_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = fraser_valley_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

fraser_valley_sp <- as(fraser_valley_sf, "Spatial")
fraser_valley_sp$ui <- 1:nrow(fraser_valley_sp@data)

coords <- coordinates(fraser_valley_sp)
fraser_valley_nb <- poly2nb(fraser_valley_sp, queen = TRUE)
## Warning in poly2nb(fraser_valley_sp, queen = TRUE): neighbour object has 2 sub-graphs;
## if this sub-graph count seems unexpected, try increasing the snap argument.
fraser_valley_nb
## Neighbour list object:
## Number of regions: 472 
## Number of nonzero links: 2822 
## Percentage nonzero weights: 1.266698 
## Average number of links: 5.978814 
## 2 disjoint connected subgraphs
#assign nearest neighbour for no links

fraser_valley_nb <- assign_nearest_neighbors(fraser_valley_nb,fraser_valley_sp)

plot(fraser_valley_sp, border = grey(0.5))
plot(fraser_valley_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(fraser_valley_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(fraser_valley_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  fraser_valley_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 8.2045, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.2194714130     -0.0021231423      0.0007294782
cyc_cc_mi <- moran.test(fraser_valley_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  fraser_valley_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 8.2775, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.2236414065     -0.0021231423      0.0007438924
pd_cc_mi <- moran.test(fraser_valley_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  fraser_valley_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 9.3134, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.2508545992     -0.0021231423      0.0007378148

BYM2 Models

nb2INLA("fraser_valley.adj", fraser_valley_nb)
g <- inla.read.graph(filename = "fraser_valley.adj")


# Model Set 1: Total Casualty Claim Crashes

fraser_valley_models_1 <- cma_models(fraser_valley_sp@data, "Fraser Valley", "n_casualty_claims", "vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
fraser_valley_all <- clean_fixed_effects(fraser_valley_models_1$fixed_effects)

map(fraser_valley_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.218, Running = 0.32, Post = 0.0963, Total = 0.634 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 2.470 0.068      2.335    2.470      2.603 2.470   0
## vandix_z    0.335 0.071      0.195    0.335      0.476 0.335   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.604 0.045       0.52    0.603      0.696 0.601
## 
## Deviance Information Criterion (DIC) ...............: 3035.43
## Deviance Information Criterion (DIC, saturated) ....: 972.17
## Effective number of parameters .....................: 448.98
## 
## Watanabe-Akaike information criterion (WAIC) ...: 3030.94
## Effective number of parameters .................: 306.12
## 
## Marginal log-Likelihood:  -2059.30 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.5, Running = 0.677, Post = 0.143, Total = 16.4 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 2.482 0.038      2.407    2.482      2.557 2.482   0
## vandix_z    0.210 0.083      0.047    0.210      0.373 0.210   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant mode
## Precision for ui 0.282 0.021      0.243    0.281      0.325 0.28
## Phi for ui       1.000 0.000      1.000    1.000      1.000 1.00
## 
## Deviance Information Criterion (DIC) ...............: 2989.21
## Deviance Information Criterion (DIC, saturated) ....: 925.94
## Effective number of parameters .....................: 424.39
## 
## Watanabe-Akaike information criterion (WAIC) ...: 2957.13
## Effective number of parameters .................: 274.73
## 
## Marginal log-Likelihood:  -1823.41 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.6, Running = 0.765, Post = 0.158, Total = 16.5 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   2.271 0.043      2.186    2.271      2.354 2.271   0
## vandix_z      0.273 0.065      0.145    0.273      0.400 0.273   0
## ln_roads_km_c 1.105 0.067      0.973    1.105      1.237 1.105   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant mode
## Precision for ui 0.708 0.068      0.583    0.705      0.852 0.70
## Phi for ui       0.804 0.054      0.683    0.809      0.894 0.82
## 
## Deviance Information Criterion (DIC) ...............: 2985.13
## Deviance Information Criterion (DIC, saturated) ....: 921.86
## Effective number of parameters .....................: 417.89
## 
## Watanabe-Akaike information criterion (WAIC) ...: 2950.41
## Effective number of parameters .................: 269.05
## 
## Marginal log-Likelihood:  -1675.37 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15.4, Running = 0.861, Post = 0.205, Total = 16.4 
## Fixed effects:
##                                mean    sd 0.025quant 0.5quant 0.975quant  mode
## (Intercept)                   2.723 0.060      2.605    2.723      2.840 2.723
## vandix_z                      0.132 0.059      0.017    0.132      0.247 0.132
## ln_roads_km_c                 0.863 0.072      0.722    0.863      1.005 0.863
## roads_prop_highway_arterial_z 0.581 0.059      0.466    0.581      0.697 0.581
## ale_index_z                   0.249 0.127      0.001    0.249      0.498 0.249
## canbics_index_z               0.181 0.141     -0.099    0.181      0.456 0.181
## population_100_c              0.027 0.012      0.002    0.026      0.051 0.026
##                               kld
## (Intercept)                     0
## vandix_z                        0
## ln_roads_km_c                   0
## roads_prop_highway_arterial_z   0
## ale_index_z                     0
## canbics_index_z                 0
## population_100_c                0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.951 0.104      0.758    0.946      1.167 0.940
## Phi for ui       0.806 0.066      0.657    0.813      0.914 0.827
## 
## Deviance Information Criterion (DIC) ...............: 2973.45
## Deviance Information Criterion (DIC, saturated) ....: 910.18
## Effective number of parameters .....................: 403.87
## 
## Watanabe-Akaike information criterion (WAIC) ...: 2931.10
## Effective number of parameters .................: 256.43
## 
## Marginal log-Likelihood:  -1641.12 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

fraser_valley_models_2 <- cma_models(fraser_valley_sp@data,"Fraser Valley","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
fraser_valley_cyclist <- clean_fixed_effects(fraser_valley_models_2$fixed_effects)

map(fraser_valley_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.18, Running = 0.305, Post = 0.0721, Total = 0.557 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.268 0.136     -1.548   -1.263     -1.013 -1.263   0
## vandix_z     0.419 0.096      0.231    0.418      0.609  0.418   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.707 0.111      0.515    0.699      0.949 0.682
## 
## Deviance Information Criterion (DIC) ...............: 1013.45
## Deviance Information Criterion (DIC, saturated) ....: 598.20
## Effective number of parameters .....................: 196.91
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1022.81
## Effective number of parameters .................: 147.69
## 
## Marginal log-Likelihood:  -564.34 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.4, Running = 0.725, Post = 0.153, Total = 16.2 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.211 0.125     -1.469   -1.207     -0.976 -1.208   0
## vandix_z     0.316 0.112      0.094    0.317      0.535  0.317   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.672 0.112      0.481    0.662      0.921 0.642
## Phi for ui       0.326 0.129      0.108    0.316      0.600 0.293
## 
## Deviance Information Criterion (DIC) ...............: 998.05
## Deviance Information Criterion (DIC, saturated) ....: 582.80
## Effective number of parameters .....................: 186.00
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1004.13
## Effective number of parameters .................: 139.05
## 
## Marginal log-Likelihood:  -315.57 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.4, Running = 0.793, Post = 0.168, Total = 16.4 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -1.353 0.123     -1.602   -1.351     -1.118 -1.351   0
## vandix_z       0.267 0.112      0.047    0.267      0.487  0.267   0
## ln_roads_km_c  0.756 0.127      0.509    0.755      1.007  0.755   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.617 0.113      0.423    0.608      0.865 0.591
## Phi for ui       0.758 0.119      0.486    0.776      0.937 0.822
## 
## Deviance Information Criterion (DIC) ...............: 960.73
## Deviance Information Criterion (DIC, saturated) ....: 545.48
## Effective number of parameters .....................: 153.40
## 
## Watanabe-Akaike information criterion (WAIC) ...: 964.76
## Effective number of parameters .................: 117.75
## 
## Marginal log-Likelihood:  -303.63 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15.5, Running = 0.842, Post = 0.181, Total = 16.5 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -0.785 0.144     -1.075   -0.783     -0.508
## vandix_z                       0.070 0.110     -0.147    0.070      0.284
## ln_roads_km_c                  0.468 0.134      0.208    0.467      0.732
## roads_prop_highway_arterial_z  0.603 0.101      0.406    0.603      0.802
## ale_index_z                    0.698 0.214      0.279    0.698      1.118
## canbics_index_z                0.092 0.299     -0.495    0.092      0.678
## population_100_c               0.046 0.023      0.001    0.046      0.091
##                                 mode kld
## (Intercept)                   -0.783   0
## vandix_z                       0.070   0
## ln_roads_km_c                  0.467   0
## roads_prop_highway_arterial_z  0.603   0
## ale_index_z                    0.698   0
## canbics_index_z                0.092   0
## population_100_c               0.046   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.893 0.185      0.585    0.874      1.310 0.837
## Phi for ui       0.615 0.159      0.283    0.628      0.883 0.666
## 
## Deviance Information Criterion (DIC) ...............: 941.57
## Deviance Information Criterion (DIC, saturated) ....: 526.32
## Effective number of parameters .....................: 136.46
## 
## Watanabe-Akaike information criterion (WAIC) ...: 942.32
## Effective number of parameters .................: 105.04
## 
## Marginal log-Likelihood:  -300.36 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

fraser_valley_models_3 <- cma_models(fraser_valley_sp@data,"Fraser Valley","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
fraser_valley_pedestrian <- clean_fixed_effects(fraser_valley_models_3$fixed_effects)

map(fraser_valley_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.213, Running = 0.331, Post = 0.0776, Total = 0.621 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.600 0.102     -0.807   -0.598     -0.406 -0.598   0
## vandix_z     0.566 0.081      0.408    0.565      0.727  0.565   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.781 0.099      0.605    0.776      0.992 0.764
## 
## Deviance Information Criterion (DIC) ...............: 1374.29
## Deviance Information Criterion (DIC, saturated) ....: 722.68
## Effective number of parameters .....................: 252.29
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1389.45
## Effective number of parameters .................: 189.47
## 
## Marginal log-Likelihood:  -773.86 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.2, Running = 0.79, Post = 0.207, Total = 16.2 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -0.577 0.095     -0.770   -0.575     -0.395 -0.575   0
## vandix_z     0.485 0.094      0.302    0.485      0.669  0.485   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.733 0.103      0.552    0.726      0.956 0.711
## Phi for ui       0.381 0.115      0.174    0.375      0.617 0.366
## 
## Deviance Information Criterion (DIC) ...............: 1347.47
## Deviance Information Criterion (DIC, saturated) ....: 695.86
## Effective number of parameters .....................: 236.95
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1354.34
## Effective number of parameters .................: 174.73
## 
## Marginal log-Likelihood:  -517.70 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.3, Running = 0.784, Post = 0.172, Total = 16.3 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -0.723 0.092     -0.906   -0.722     -0.545 -0.722   0
## vandix_z       0.431 0.090      0.255    0.431      0.608  0.431   0
## ln_roads_km_c  0.815 0.104      0.610    0.816      1.019  0.816   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.654 0.102      0.473    0.648      0.873 0.637
## Phi for ui       0.856 0.085      0.646    0.873      0.971 0.915
## 
## Deviance Information Criterion (DIC) ...............: 1296.05
## Deviance Information Criterion (DIC, saturated) ....: 644.44
## Effective number of parameters .....................: 194.29
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1294.06
## Effective number of parameters .................: 143.15
## 
## Marginal log-Likelihood:  -495.51 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15.2, Running = 0.818, Post = 0.249, Total = 16.3 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -0.205 0.113     -0.431   -0.203      0.014
## vandix_z                       0.270 0.086      0.102    0.270      0.438
## ln_roads_km_c                  0.422 0.114      0.199    0.421      0.646
## roads_prop_highway_arterial_z  0.622 0.082      0.461    0.621      0.784
## ale_index_z                    0.494 0.178      0.146    0.494      0.842
## canbics_index_z                0.021 0.239     -0.449    0.021      0.489
## population_100_c               0.059 0.019      0.023    0.059      0.097
##                                 mode kld
## (Intercept)                   -0.203   0
## vandix_z                       0.270   0
## ln_roads_km_c                  0.421   0
## roads_prop_highway_arterial_z  0.621   0
## ale_index_z                    0.494   0
## canbics_index_z                0.021   0
## population_100_c               0.059   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean   sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.041 0.18      0.730    1.026      1.435 0.999
## Phi for ui       0.678 0.13      0.395    0.691      0.893 0.723
## 
## Deviance Information Criterion (DIC) ...............: 1271.84
## Deviance Information Criterion (DIC, saturated) ....: 620.23
## Effective number of parameters .....................: 174.02
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1264.96
## Effective number of parameters .................: 127.05
## 
## Marginal log-Likelihood:  -483.15 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
fraser_valley_results <- bind_rows(fraser_valley_all %>% mutate(Region = "Fraser Valley",Outcome = "All Injury Claims"),
                         fraser_valley_cyclist %>% mutate(Region = "Fraser Valley",Outcome = "Cyclist Injury Claims"),
                         fraser_valley_pedestrian %>% mutate(Region = "Fraser Valley",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

North Central

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

North Central

n_claims

350

31,422.0

89.8

182.3

0.0

1,906.0

0

13

3.7

n_casualty_claims

4,490.0

12.8

25.4

0.0

228.0

0

48

13.7

n_cyclist_claims

107.0

0.3

1.0

0.0

11.0

0

287

82.0

n_cyclist_casualty_claims

54.0

0.2

0.6

0.0

5.0

0

314

89.7

n_pedestrian_claims

241.0

0.7

2.0

0.0

27.0

0

240

68.6

n_pedestrian_casualty_claims

203.0

0.6

1.6

0.0

21.0

0

253

72.3

population

182,780.0

525.2

277.1

0.0

2,479.0

2

4

1.1

total_roads_km

9,989.6

28.5

54.4

0.9

398.4

0

0

0.0

roads_prop_highway_arterial

45.4

0.1

0.1

0.0

0.7

0

132

37.7

no_highschool_prevalance

74.8

0.2

0.1

0.1

0.8

21

0

0.0

unemployment_rate

3,459.5

10.5

6.8

0.0

60.0

21

14

4.0

hh_avg_income

24,402,848.0

77,716.1

21,870.6

34,760.0

201,050.0

36

0

0.0

participation_rate

22,327.9

67.9

9.3

35.7

89.8

21

0

0.0

university_degree_prevalance

149.0

0.5

0.1

0.0

0.7

21

1

0.3

lone_parent_fam_prevalence

60.1

0.2

0.1

0.0

0.6

20

0

0.0

home_owner_prevalence

233.8

0.7

0.2

0.0

1.0

21

4

1.1

vandix

156.6

0.5

0.7

-1.0

3.4

36

0

0.0

ale_index

-387.8

-1.3

0.6

-2.1

0.0

56

0

0.0

canbics_index

183.2

0.6

1.0

0.0

4.9

35

179

51.1

Maps

claims <- ggplot() + 
  geom_sf(data = north_central_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = north_central_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = north_central_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

north_central_sp <- as(north_central_sf, "Spatial")
north_central_sp$ui <- 1:nrow(north_central_sp@data)

coords <- coordinates(north_central_sp)
north_central_nb <- poly2nb(north_central_sp, queen = TRUE)

north_central_nb
## Neighbour list object:
## Number of regions: 350 
## Number of nonzero links: 1934 
## Percentage nonzero weights: 1.578776 
## Average number of links: 5.525714
#assign nearest neighbour for no links

north_central_nb <- assign_nearest_neighbors(north_central_nb,north_central_sp)

plot(north_central_sp, border = grey(0.5))
plot(north_central_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(north_central_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(north_central_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  north_central_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 7.4904, p-value = 3.433e-14
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.234880440      -0.002865330       0.001007426
cyc_cc_mi <- moran.test(north_central_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  north_central_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 3.6381, p-value = 0.0001373
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.113990179      -0.002865330       0.001031689
pd_cc_mi <- moran.test(north_central_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  north_central_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 6.4778, p-value = 4.652e-11
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##      0.1909270561     -0.0028653295      0.0008949772

BYM2 Models

nb2INLA("north_central.adj", north_central_nb)
g <- inla.read.graph(filename = "north_central.adj")


# Model Set 1: Total Casualty Claim Crashes

north_central_models_1 <- cma_models(north_central_sp@data, "North Central", "n_casualty_claims", "vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
north_central_all <- clean_fixed_effects(north_central_models_1$fixed_effects)

map(north_central_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.26, Running = 0.279, Post = 0.0786, Total = 0.617 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 1.385 0.099      1.188    1.386      1.576 1.386   0
## vandix_z    0.294 0.072      0.153    0.293      0.436 0.293   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.537 0.052       0.44    0.535      0.645 0.531
## 
## Deviance Information Criterion (DIC) ...............: 1877.78
## Deviance Information Criterion (DIC, saturated) ....: 724.91
## Effective number of parameters .....................: 314.28
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1926.75
## Effective number of parameters .................: 245.94
## 
## Marginal log-Likelihood:  -1219.26 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.8, Running = 0.591, Post = 0.135, Total = 15.5 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 1.441 0.081      1.280    1.442      1.597 1.442   0
## vandix_z    0.166 0.074      0.021    0.166      0.312 0.166   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.308 0.048      0.224    0.305      0.412 0.298
## Phi for ui       0.774 0.067      0.624    0.781      0.886 0.796
## 
## Deviance Information Criterion (DIC) ...............: 1836.90
## Deviance Information Criterion (DIC, saturated) ....: 684.03
## Effective number of parameters .....................: 299.06
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1859.14
## Effective number of parameters .................: 219.53
## 
## Marginal log-Likelihood:  -1102.65 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.2, Running = 0.587, Post = 0.166, Total = 16 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   0.699 0.134      0.433    0.700      0.960 0.700   0
## vandix_z      0.246 0.071      0.108    0.246      0.385 0.246   0
## ln_roads_km_c 0.656 0.093      0.474    0.656      0.839 0.656   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.236 0.033      0.175    0.234      0.304 0.233
## Phi for ui       0.943 0.034      0.856    0.950      0.987 0.965
## 
## Deviance Information Criterion (DIC) ...............: 1798.49
## Deviance Information Criterion (DIC, saturated) ....: 645.62
## Effective number of parameters .....................: 282.37
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1793.36
## Effective number of parameters .................: 192.21
## 
## Marginal log-Likelihood:  -1084.45 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14.8, Running = 0.659, Post = 0.187, Total = 15.7 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                    1.197 0.224      0.754    1.197      1.634
## vandix_z                       0.177 0.066      0.048    0.177      0.306
## ln_roads_km_c                  0.497 0.089      0.321    0.497      0.672
## roads_prop_highway_arterial_z  0.631 0.086      0.463    0.631      0.800
## ale_index_z                   -0.204 0.294     -0.780   -0.204      0.375
## canbics_index_z                0.429 0.312     -0.183    0.429      1.040
## population_100_c               0.034 0.022     -0.007    0.034      0.077
##                                 mode kld
## (Intercept)                    1.197   0
## vandix_z                       0.177   0
## ln_roads_km_c                  0.497   0
## roads_prop_highway_arterial_z  0.631   0
## ale_index_z                   -0.204   0
## canbics_index_z                0.429   0
## population_100_c               0.034   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.276 0.037      0.208    0.275      0.354 0.274
## Phi for ui       0.955 0.031      0.876    0.962      0.992 0.977
## 
## Deviance Information Criterion (DIC) ...............: 1791.38
## Deviance Information Criterion (DIC, saturated) ....: 638.51
## Effective number of parameters .....................: 272.89
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1779.75
## Effective number of parameters .................: 183.19
## 
## Marginal log-Likelihood:  -1080.19 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

north_central_models_2 <- cma_models(north_central_sp@data,"North Central","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
north_central_cyclist <- clean_fixed_effects(north_central_models_2$fixed_effects)

map(north_central_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.18, Running = 0.261, Post = 0.0718, Total = 0.513 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -2.097 0.178     -2.446   -2.097     -1.749 -2.097   0
## vandix_z     0.238 0.108      0.027    0.238      0.450  0.238   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                      mean       sd 0.025quant 0.5quant 0.975quant   mode
## Precision for ui 19896.21 19932.69     586.12 13845.55   73915.10 206.69
## 
## Deviance Information Criterion (DIC) ...............: 342.46
## Deviance Information Criterion (DIC, saturated) ....: 261.09
## Effective number of parameters .....................: 1.98
## 
## Watanabe-Akaike information criterion (WAIC) ...: 343.92
## Effective number of parameters .................: 3.40
## 
## Marginal log-Likelihood:  -176.09 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.4, Running = 0.619, Post = 0.144, Total = 15.2 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -3.068 0.343     -3.833   -3.049     -2.443 -3.056   0
## vandix_z     0.276 0.137      0.011    0.275      0.547  0.275   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.660 0.206      0.352    0.628      1.155 0.568
## Phi for ui       0.162 0.112      0.024    0.135      0.449 0.073
## 
## Deviance Information Criterion (DIC) ...............: 276.93
## Deviance Information Criterion (DIC, saturated) ....: 195.56
## Effective number of parameters .....................: 52.45
## 
## Watanabe-Akaike information criterion (WAIC) ...: 281.59
## Effective number of parameters .................: 43.08
## 
## Marginal log-Likelihood:  -80.58 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15, Running = 0.649, Post = 0.139, Total = 15.8 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -3.239 0.399     -4.089   -3.221     -2.504 -3.225   0
## vandix_z       0.307 0.143      0.029    0.306      0.591  0.306   0
## ln_roads_km_c  0.127 0.162     -0.188    0.125      0.449  0.125   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.647 0.202      0.344    0.615      1.133 0.556
## Phi for ui       0.195 0.128      0.031    0.165      0.516 0.093
## 
## Deviance Information Criterion (DIC) ...............: 276.46
## Deviance Information Criterion (DIC, saturated) ....: 195.08
## Effective number of parameters .....................: 51.62
## 
## Watanabe-Akaike information criterion (WAIC) ...: 281.36
## Effective number of parameters .................: 42.86
## 
## Marginal log-Likelihood:  -85.57 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14.9, Running = 0.826, Post = 0.204, Total = 16 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -2.309 0.496     -3.320   -2.296     -1.373
## vandix_z                       0.304 0.145      0.022    0.303      0.593
## ln_roads_km_c                  0.171 0.177     -0.174    0.170      0.521
## roads_prop_highway_arterial_z  0.522 0.195      0.141    0.520      0.908
## ale_index_z                   -0.216 0.711     -1.609   -0.217      1.184
## canbics_index_z                1.982 0.558      0.896    1.979      3.090
## population_100_c              -0.072 0.080     -0.230   -0.072      0.085
##                                 mode kld
## (Intercept)                   -2.297   0
## vandix_z                       0.303   0
## ln_roads_km_c                  0.170   0
## roads_prop_highway_arterial_z  0.520   0
## ale_index_z                   -0.217   0
## canbics_index_z                1.979   0
## population_100_c              -0.072   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.890 0.339      0.417    0.827      1.731 0.714
## Phi for ui       0.288 0.162      0.055    0.260      0.663 0.173
## 
## Deviance Information Criterion (DIC) ...............: 272.38
## Deviance Information Criterion (DIC, saturated) ....: 191.01
## Effective number of parameters .....................: 41.88
## 
## Watanabe-Akaike information criterion (WAIC) ...: 280.15
## Effective number of parameters .................: 38.90
## 
## Marginal log-Likelihood:  -93.94 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

north_central_models_3 <- cma_models(north_central_sp@data,"North Central","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
north_central_pedestrian <- clean_fixed_effects(north_central_models_3$fixed_effects)

map(north_central_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.21, Running = 0.357, Post = 0.0769, Total = 0.644 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.974 0.225     -2.452   -1.962     -1.566 -1.928   0
## vandix_z     0.424 0.102      0.227    0.423      0.627  0.423   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.563 0.109      0.378    0.553      0.802 0.534
## 
## Deviance Information Criterion (DIC) ...............: 613.58
## Deviance Information Criterion (DIC, saturated) ....: 380.61
## Effective number of parameters .....................: 132.57
## 
## Watanabe-Akaike information criterion (WAIC) ...: 627.32
## Effective number of parameters .................: 102.18
## 
## Marginal log-Likelihood:  -350.09 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.7, Running = 0.606, Post = 0.141, Total = 15.5 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.865 0.195     -2.274   -1.857     -1.503 -1.858   0
## vandix_z     0.350 0.103      0.148    0.350      0.553  0.350   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.555 0.127      0.349    0.541      0.847 0.512
## Phi for ui       0.357 0.154      0.102    0.343      0.683 0.303
## 
## Deviance Information Criterion (DIC) ...............: 589.79
## Deviance Information Criterion (DIC, saturated) ....: 356.82
## Effective number of parameters .....................: 113.83
## 
## Watanabe-Akaike information criterion (WAIC) ...: 592.02
## Effective number of parameters .................: 84.15
## 
## Marginal log-Likelihood:  -257.75 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 14.8, Running = 0.681, Post = 0.21, Total = 15.7 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -1.945 0.242     -2.444   -1.938     -1.491 -1.938   0
## vandix_z       0.355 0.105      0.150    0.355      0.563  0.355   0
## ln_roads_km_c  0.071 0.140     -0.195    0.067      0.358  0.068   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.531 0.134      0.317    0.514      0.843 0.481
## Phi for ui       0.415 0.181      0.107    0.404      0.778 0.366
## 
## Deviance Information Criterion (DIC) ...............: 588.24
## Deviance Information Criterion (DIC, saturated) ....: 355.27
## Effective number of parameters .....................: 112.40
## 
## Watanabe-Akaike information criterion (WAIC) ...: 590.74
## Effective number of parameters .................: 83.54
## 
## Marginal log-Likelihood:  -263.12 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14.7, Running = 0.668, Post = 0.192, Total = 15.6 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -1.894 0.446     -2.803   -1.882     -1.052
## vandix_z                       0.301 0.105      0.095    0.300      0.509
## ln_roads_km_c                 -0.097 0.160     -0.402   -0.100      0.228
## roads_prop_highway_arterial_z  0.659 0.146      0.375    0.658      0.946
## ale_index_z                   -1.045 0.632     -2.309   -1.037      0.173
## canbics_index_z                0.649 0.495     -0.317    0.646      1.629
## population_100_c               0.017 0.044     -0.069    0.017      0.105
##                                 mode kld
## (Intercept)                   -1.883   0
## vandix_z                       0.300   0
## ln_roads_km_c                 -0.100   0
## roads_prop_highway_arterial_z  0.658   0
## ale_index_z                   -1.037   0
## canbics_index_z                0.646   0
## population_100_c               0.017   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.546 0.155      0.303    0.525      0.909 0.486
## Phi for ui       0.528 0.188      0.170    0.532      0.865 0.547
## 
## Deviance Information Criterion (DIC) ...............: 575.52
## Deviance Information Criterion (DIC, saturated) ....: 342.56
## Effective number of parameters .....................: 102.83
## 
## Watanabe-Akaike information criterion (WAIC) ...: 578.07
## Effective number of parameters .................: 77.72
## 
## Marginal log-Likelihood:  -271.38 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
north_central_results <- bind_rows(north_central_all %>% mutate(Region = "North Central",Outcome = "All Injury Claims"),
                         north_central_cyclist %>% mutate(Region = "North Central",Outcome = "Cyclist Injury Claims"),
                         north_central_pedestrian %>% mutate(Region = "North Central",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

Kamloops-Salmon Arm

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

Kamloops-Salmon Arm

n_claims

204

24,765.0

121.4

244.3

0.0

2,286.0

0

5

2.5

n_casualty_claims

4,069.0

19.9

39.5

0.0

293.0

0

19

9.3

n_cyclist_claims

143.0

0.7

1.7

0.0

14.0

0

138

67.6

n_cyclist_casualty_claims

89.0

0.4

1.1

0.0

10.0

0

152

74.5

n_pedestrian_claims

236.0

1.2

2.9

0.0

21.0

0

130

63.7

n_pedestrian_casualty_claims

183.0

0.9

2.3

0.0

17.0

0

137

67.2

population

133,847.0

656.1

348.0

0.0

2,310.0

0

2

1.0

total_roads_km

2,744.5

13.5

25.3

0.5

217.0

0

0

0.0

roads_prop_highway_arterial

49.9

0.2

0.2

0.0

0.7

0

32

15.7

no_highschool_prevalance

29.4

0.2

0.1

0.0

0.4

31

0

0.0

unemployment_rate

1,439.0

8.3

5.3

0.0

37.5

31

12

5.9

hh_avg_income

12,008,631.0

71,479.9

20,375.9

29,162.0

137,275.0

36

0

0.0

participation_rate

10,775.2

62.3

9.9

30.6

90.0

31

0

0.0

university_degree_prevalance

88.4

0.5

0.1

0.3

0.7

31

0

0.0

lone_parent_fam_prevalence

31.0

0.2

0.1

0.0

0.5

30

0

0.0

home_owner_prevalence

128.1

0.7

0.2

0.1

1.0

31

0

0.0

vandix

30.5

0.2

0.7

-1.3

2.4

36

0

0.0

ale_index

-116.3

-0.7

1.2

-2.1

3.3

41

1

0.5

canbics_index

227.8

1.4

1.5

0.0

5.6

41

40

19.6

Maps

claims <- ggplot() + 
  geom_sf(data = interior_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = interior_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = interior_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

interior_sp <- as(interior_sf, "Spatial")
interior_sp$ui <- 1:nrow(interior_sp@data)

coords <- coordinates(interior_sp)
interior_nb <- poly2nb(interior_sp, queen = TRUE)
## Warning in poly2nb(interior_sp, queen = TRUE): neighbour object has 3 sub-graphs;
## if this sub-graph count seems unexpected, try increasing the snap argument.
interior_nb
## Neighbour list object:
## Number of regions: 204 
## Number of nonzero links: 1098 
## Percentage nonzero weights: 2.638408 
## Average number of links: 5.382353 
## 3 disjoint connected subgraphs
#assign nearest neighbour for no links

interior_nb <- assign_nearest_neighbors(interior_nb,interior_sp)

plot(interior_sp, border = grey(0.5))
plot(interior_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(interior_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(interior_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  interior_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 6.3114, p-value = 1.383e-10
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.261379586      -0.004926108       0.001780360
cyc_cc_mi <- moran.test(interior_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  interior_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 2.4815, p-value = 0.006542
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.096406801      -0.004926108       0.001667545
pd_cc_mi <- moran.test(interior_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  interior_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 4.6131, p-value = 1.983e-06
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.190275369      -0.004926108       0.001790493

BYM2 Models

nb2INLA("interior.adj", interior_nb)
g <- inla.read.graph(filename = "interior.adj")


# Model Set 1: Total Casualty Claim Crashes

interior_models_1 <- cma_models(interior_sp@data, "Kamloops-Salmon Arm", "n_casualty_claims", "vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
interior_all <- clean_fixed_effects(interior_models_1$fixed_effects)

map(interior_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.206, Running = 0.248, Post = 0.0771, Total = 0.531 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 1.936 0.105      1.728    1.937      2.139 1.937   0
## vandix_z    0.379 0.103      0.178    0.379      0.581 0.379   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.565 0.068      0.441    0.562      0.708 0.556
## 
## Deviance Information Criterion (DIC) ...............: 1187.06
## Deviance Information Criterion (DIC, saturated) ....: 422.26
## Effective number of parameters .....................: 187.60
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1199.03
## Effective number of parameters .................: 136.48
## 
## Marginal log-Likelihood:  -796.51 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.7, Running = 0.509, Post = 0.131, Total = 15.4 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 1.953 0.082      1.790    1.954      2.112 1.954   0
## vandix_z    0.244 0.115      0.019    0.245      0.469 0.245   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.646 0.083      0.497    0.641      0.824 0.631
## Phi for ui       0.421 0.107      0.223    0.418      0.639 0.410
## 
## Deviance Information Criterion (DIC) ...............: 1176.12
## Deviance Information Criterion (DIC, saturated) ....: 411.33
## Effective number of parameters .....................: 182.32
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1181.65
## Effective number of parameters .................: 129.27
## 
## Marginal log-Likelihood:  -647.10 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 14.6, Running = 0.521, Post = 0.179, Total = 15.3 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   1.431 0.099      1.235    1.432      1.625 1.432   0
## vandix_z      0.249 0.103      0.047    0.249      0.451 0.249   0
## ln_roads_km_c 0.850 0.106      0.643    0.849      1.059 0.849   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.773 0.104      0.588    0.767      0.996 0.756
## Phi for ui       0.627 0.097      0.427    0.632      0.804 0.639
## 
## Deviance Information Criterion (DIC) ...............: 1158.32
## Deviance Information Criterion (DIC, saturated) ....: 393.52
## Effective number of parameters .....................: 172.42
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1151.71
## Effective number of parameters .................: 115.91
## 
## Marginal log-Likelihood:  -622.89 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 15, Running = 0.493, Post = 0.16, Total = 15.6 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                    1.134 0.119      0.900    1.134      1.368
## vandix_z                       0.199 0.084      0.034    0.199      0.365
## ln_roads_km_c                  0.492 0.097      0.303    0.492      0.682
## roads_prop_highway_arterial_z  0.535 0.056      0.425    0.535      0.646
## ale_index_z                    0.092 0.257     -0.412    0.092      0.596
## canbics_index_z               -0.709 0.249     -1.199   -0.708     -0.220
## population_100_c               0.099 0.019      0.062    0.099      0.135
##                                 mode kld
## (Intercept)                    1.134   0
## vandix_z                       0.199   0
## ln_roads_km_c                  0.492   0
## roads_prop_highway_arterial_z  0.535   0
## ale_index_z                    0.092   0
## canbics_index_z               -0.708   0
## population_100_c               0.099   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                  mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.17 0.170      0.867    1.161      1.534 1.145
## Phi for ui       0.82 0.085      0.622    0.833      0.948 0.864
## 
## Deviance Information Criterion (DIC) ...............: 1138.19
## Deviance Information Criterion (DIC, saturated) ....: 373.39
## Effective number of parameters .....................: 154.83
## 
## Watanabe-Akaike information criterion (WAIC) ...: 1123.47
## Effective number of parameters .................: 100.55
## 
## Marginal log-Likelihood:  -598.24 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

interior_models_2 <- cma_models(interior_sp@data,"Kamloops-Salmon Arm","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
interior_cyclist <- clean_fixed_effects(interior_models_2$fixed_effects)

map(interior_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.192, Running = 0.252, Post = 0.0682, Total = 0.512 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.703 0.241     -2.216   -1.690     -1.270 -1.653   0
## vandix_z     0.456 0.141      0.182    0.455      0.737  0.455   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.921 0.324      0.468    0.863       1.71 0.769
## 
## Deviance Information Criterion (DIC) ...............: 324.99
## Deviance Information Criterion (DIC, saturated) ....: 204.25
## Effective number of parameters .....................: 56.16
## 
## Watanabe-Akaike information criterion (WAIC) ...: 326.11
## Effective number of parameters .................: 43.18
## 
## Marginal log-Likelihood:  -187.90 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.7, Running = 0.519, Post = 0.103, Total = 15.3 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.615 0.208     -2.054   -1.608     -1.228 -1.609   0
## vandix_z     0.358 0.154      0.051    0.360      0.655  0.360   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.052 0.330      0.560    1.001      1.845 0.904
## Phi for ui       0.214 0.132      0.035    0.187      0.531 0.112
## 
## Deviance Information Criterion (DIC) ...............: 323.34
## Deviance Information Criterion (DIC, saturated) ....: 202.60
## Effective number of parameters .....................: 50.44
## 
## Watanabe-Akaike information criterion (WAIC) ...: 325.36
## Effective number of parameters .................: 40.43
## 
## Marginal log-Likelihood:  -58.61 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 14.4, Running = 0.508, Post = 0.118, Total = 15 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -2.039 0.278     -2.618   -2.029     -1.522 -2.030   0
## vandix_z       0.376 0.162      0.053    0.378      0.691  0.378   0
## ln_roads_km_c  0.585 0.201      0.198    0.582      0.991  0.582   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.053 0.343      0.546    0.998      1.880 0.896
## Phi for ui       0.523 0.194      0.162    0.525      0.874 0.522
## 
## Deviance Information Criterion (DIC) ...............: 316.65
## Deviance Information Criterion (DIC, saturated) ....: 195.92
## Effective number of parameters .....................: 45.88
## 
## Watanabe-Akaike information criterion (WAIC) ...: 318.61
## Effective number of parameters .................: 37.30
## 
## Marginal log-Likelihood:  -59.43 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14.4, Running = 0.492, Post = 0.143, Total = 15 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -1.916 0.325     -2.588   -1.904     -1.314
## vandix_z                       0.372 0.176      0.017    0.376      0.706
## ln_roads_km_c                  0.195 0.217     -0.225    0.193      0.626
## roads_prop_highway_arterial_z  0.399 0.138      0.130    0.399      0.673
## ale_index_z                    0.639 0.489     -0.333    0.644      1.588
## canbics_index_z               -0.277 0.491     -1.235   -0.280      0.693
## population_100_c               0.141 0.038      0.066    0.140      0.217
##                                 mode kld
## (Intercept)                   -1.904   0
## vandix_z                       0.376   0
## ln_roads_km_c                  0.193   0
## roads_prop_highway_arterial_z  0.399   0
## ale_index_z                    0.644   0
## canbics_index_z               -0.280   0
## population_100_c               0.140   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.806 0.867      0.713    1.616       4.03 1.303
## Phi for ui       0.627 0.215      0.180    0.654       0.95 0.808
## 
## Deviance Information Criterion (DIC) ...............: 308.18
## Deviance Information Criterion (DIC, saturated) ....: 187.44
## Effective number of parameters .....................: 34.53
## 
## Watanabe-Akaike information criterion (WAIC) ...: 311.12
## Effective number of parameters .................: 30.56
## 
## Marginal log-Likelihood:  -66.39 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

interior_models_3 <- cma_models(interior_sp@data,"Kamloops-Salmon Arm","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
interior_pedestrian <- clean_fixed_effects(interior_models_3$fixed_effects)

map(interior_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.18, Running = 0.24, Post = 0.0535, Total = 0.473 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.597 0.248     -2.134   -1.581     -1.155 -1.544   0
## vandix_z     0.687 0.149      0.402    0.685      0.988  0.685   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.506 0.114      0.316    0.495      0.761 0.473
## 
## Deviance Information Criterion (DIC) ...............: 421.56
## Deviance Information Criterion (DIC, saturated) ....: 250.11
## Effective number of parameters .....................: 92.33
## 
## Watanabe-Akaike information criterion (WAIC) ...: 439.84
## Effective number of parameters .................: 75.38
## 
## Marginal log-Likelihood:  -251.71 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14, Running = 0.444, Post = 0.113, Total = 14.6 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.465 0.201     -1.888   -1.457     -1.092 -1.458   0
## vandix_z     0.649 0.159      0.340    0.648      0.964  0.648   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.625 0.133      0.404    0.611      0.923 0.586
## Phi for ui       0.271 0.125      0.077    0.254      0.552 0.211
## 
## Deviance Information Criterion (DIC) ...............: 415.60
## Deviance Information Criterion (DIC, saturated) ....: 244.14
## Effective number of parameters .....................: 81.08
## 
## Watanabe-Akaike information criterion (WAIC) ...: 423.72
## Effective number of parameters .................: 63.38
## 
## Marginal log-Likelihood:  -121.89 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 14.8, Running = 0.471, Post = 0.158, Total = 15.4 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -1.851 0.243     -2.351   -1.844     -1.395 -1.845   0
## vandix_z       0.685 0.161      0.371    0.684      1.002  0.684   0
## ln_roads_km_c  0.619 0.181      0.267    0.618      0.979  0.618   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.674 0.151      0.425    0.657      1.016 0.626
## Phi for ui       0.478 0.155      0.194    0.475      0.781 0.459
## 
## Deviance Information Criterion (DIC) ...............: 408.89
## Deviance Information Criterion (DIC, saturated) ....: 237.43
## Effective number of parameters .....................: 73.23
## 
## Watanabe-Akaike information criterion (WAIC) ...: 414.90
## Effective number of parameters .................: 57.59
## 
## Marginal log-Likelihood:  -121.52 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14.9, Running = 0.507, Post = 0.128, Total = 15.5 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -1.577 0.290     -2.171   -1.569     -1.034
## vandix_z                       0.659 0.152      0.359    0.659      0.957
## ln_roads_km_c                  0.245 0.189     -0.124    0.243      0.619
## roads_prop_highway_arterial_z  0.393 0.123      0.152    0.392      0.636
## ale_index_z                    1.571 0.451      0.680    1.573      2.452
## canbics_index_z               -0.979 0.452     -1.877   -0.976     -0.099
## population_100_c               0.111 0.037      0.039    0.111      0.184
##                                 mode kld
## (Intercept)                   -1.569   0
## vandix_z                       0.659   0
## ln_roads_km_c                  0.243   0
## roads_prop_highway_arterial_z  0.392   0
## ale_index_z                    1.573   0
## canbics_index_z               -0.976   0
## population_100_c               0.111   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.084 0.314      0.602    1.039      1.826 0.953
## Phi for ui       0.379 0.197      0.067    0.359      0.786 0.264
## 
## Deviance Information Criterion (DIC) ...............: 400.81
## Deviance Information Criterion (DIC, saturated) ....: 229.36
## Effective number of parameters .....................: 61.30
## 
## Watanabe-Akaike information criterion (WAIC) ...: 404.56
## Effective number of parameters .................: 49.26
## 
## Marginal log-Likelihood:  -125.77 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
interior_results <- bind_rows(interior_all %>% mutate(Region = "Kamloops-Salmon Arm",Outcome = "All Injury Claims"),
                         interior_cyclist %>% mutate(Region = "Kamloops-Salmon Arm",Outcome = "Cyclist Injury Claims"),
                         interior_pedestrian %>% mutate(Region = "Kamloops-Salmon Arm",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

Southeast

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

Southeast

n_claims

108

9,978.0

92.4

171.3

0.0

1,235.0

0

3

2.8

n_casualty_claims

1,037.0

9.6

17.9

0.0

121.0

0

12

11.1

n_cyclist_claims

40.0

0.4

0.8

0.0

4.0

0

85

78.7

n_cyclist_casualty_claims

24.0

0.2

0.6

0.0

4.0

0

92

85.2

n_pedestrian_claims

62.0

0.6

1.3

0.0

8.0

0

77

71.3

n_pedestrian_casualty_claims

51.0

0.5

1.2

0.0

8.0

0

83

76.9

population

60,427.0

559.5

202.6

0.0

1,482.0

0

2

1.9

total_roads_km

1,598.6

14.8

23.9

1.3

202.4

0

0

0.0

roads_prop_highway_arterial

13.9

0.1

0.2

0.0

0.5

0

49

45.4

no_highschool_prevalance

16.2

0.2

0.1

0.0

0.3

4

0

0.0

unemployment_rate

838.5

8.1

4.4

0.0

17.5

4

9

8.3

hh_avg_income

7,149,722.0

68,747.3

16,755.0

34,159.0

122,980.0

4

0

0.0

participation_rate

6,473.1

62.2

8.5

40.9

80.0

4

0

0.0

university_degree_prevalance

57.1

0.5

0.1

0.3

0.7

4

0

0.0

lone_parent_fam_prevalence

17.1

0.2

0.1

0.0

0.4

4

0

0.0

home_owner_prevalence

77.2

0.7

0.2

0.0

1.0

4

1

0.9

vandix

8.2

0.1

0.6

-0.9

1.6

4

0

0.0

ale_index

-125.7

-1.2

0.7

-2.1

0.4

7

0

0.0

canbics_index

32.4

0.3

0.5

0.0

2.0

7

64

59.3

Maps

claims <- ggplot() + 
  geom_sf(data = southeast_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = southeast_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = southeast_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

southeast_sp <- as(southeast_sf, "Spatial")
southeast_sp$ui <- 1:nrow(southeast_sp@data)

coords <- coordinates(southeast_sp)
southeast_nb <- poly2nb(southeast_sp, queen = TRUE)
## Warning in poly2nb(southeast_sp, queen = TRUE): neighbour object has 3 sub-graphs;
## if this sub-graph count seems unexpected, try increasing the snap argument.
southeast_nb
## Neighbour list object:
## Number of regions: 108 
## Number of nonzero links: 548 
## Percentage nonzero weights: 4.698217 
## Average number of links: 5.074074 
## 3 disjoint connected subgraphs
#assign nearest neighbour for no links

southeast_nb <- assign_nearest_neighbors(southeast_nb,southeast_sp)

plot(southeast_sp, border = grey(0.5))
plot(southeast_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(southeast_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(southeast_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  southeast_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 2.6818, p-value = 0.003661
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.143726600      -0.009345794       0.003257898
cyc_cc_mi <- moran.test(southeast_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  southeast_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 0.61539, p-value = 0.2691
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.026276623      -0.009345794       0.003350726
pd_cc_mi <- moran.test(southeast_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  southeast_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 2.1151, p-value = 0.01721
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.111266178      -0.009345794       0.003251770

BYM2 Models

nb2INLA("southeast.adj", southeast_nb)
g <- inla.read.graph(filename = "southeast.adj")


# Model Set 1: Total Casualty Claim Crashes

southeast_models_1 <- cma_models(southeast_sp@data, "Southeast", "n_casualty_claims", "vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
southeast_all <- clean_fixed_effects(southeast_models_1$fixed_effects)

map(southeast_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.181, Running = 0.221, Post = 0.0696, Total = 0.472 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 1.313 0.135      1.041    1.315      1.571 1.315   0
## vandix_z    0.500 0.144      0.219    0.499      0.783 0.499   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.708 0.124       0.49    0.699      0.976 0.681
## 
## Deviance Information Criterion (DIC) ...............: 544.56
## Deviance Information Criterion (DIC, saturated) ....: 208.25
## Effective number of parameters .....................: 90.53
## 
## Watanabe-Akaike information criterion (WAIC) ...: 548.83
## Effective number of parameters .................: 65.15
## 
## Marginal log-Likelihood:  -352.71 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 15.2, Running = 0.347, Post = 0.138, Total = 15.7 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 1.317 0.110      1.096    1.319      1.529 1.318   0
## vandix_z    0.363 0.148      0.072    0.363      0.653 0.363   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.778 0.132      0.549    0.767       1.07 0.748
## Phi for ui       0.387 0.145      0.138    0.377       0.69 0.347
## 
## Deviance Information Criterion (DIC) ...............: 540.42
## Deviance Information Criterion (DIC, saturated) ....: 204.12
## Effective number of parameters .....................: 88.58
## 
## Watanabe-Akaike information criterion (WAIC) ...: 543.69
## Effective number of parameters .................: 63.22
## 
## Marginal log-Likelihood:  -264.51 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 14.9, Running = 0.37, Post = 0.135, Total = 15.4 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   0.761 0.165      0.435    0.762      1.082 0.762   0
## vandix_z      0.394 0.140      0.121    0.393      0.670 0.393   0
## ln_roads_km_c 0.707 0.160      0.396    0.706      1.024 0.706   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.855 0.151      0.593    0.843      1.185 0.822
## Phi for ui       0.643 0.152      0.326    0.655      0.897 0.686
## 
## Deviance Information Criterion (DIC) ...............: 530.54
## Deviance Information Criterion (DIC, saturated) ....: 194.23
## Effective number of parameters .....................: 83.73
## 
## Watanabe-Akaike information criterion (WAIC) ...: 527.56
## Effective number of parameters .................: 56.37
## 
## Marginal log-Likelihood:  -260.11 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14.8, Running = 0.39, Post = 0.173, Total = 15.4 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                    1.752 0.406      0.950    1.754      2.545
## vandix_z                       0.367 0.131      0.112    0.367      0.626
## ln_roads_km_c                  0.450 0.183      0.093    0.448      0.813
## roads_prop_highway_arterial_z  0.570 0.152      0.271    0.571      0.868
## ale_index_z                    1.651 0.821      0.043    1.649      3.271
## canbics_index_z               -0.567 0.854     -2.247   -0.566      1.108
## population_100_c               0.143 0.059      0.028    0.143      0.260
##                                 mode kld
## (Intercept)                    1.754   0
## vandix_z                       0.367   0
## ln_roads_km_c                  0.449   0
## roads_prop_highway_arterial_z  0.571   0
## ale_index_z                    1.649   0
## canbics_index_z               -0.567   0
## population_100_c               0.143   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.031 0.188      0.708    1.015      1.444 0.986
## Phi for ui       0.679 0.144      0.367    0.694      0.912 0.736
## 
## Deviance Information Criterion (DIC) ...............: 526.65
## Deviance Information Criterion (DIC, saturated) ....: 190.34
## Effective number of parameters .....................: 80.38
## 
## Watanabe-Akaike information criterion (WAIC) ...: 521.47
## Effective number of parameters .................: 53.13
## 
## Marginal log-Likelihood:  -268.71 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

southeast_models_2 <- cma_models(southeast_sp@data,"Southeast","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
southeast_cyclist <- clean_fixed_effects(southeast_models_2$fixed_effects)

map(southeast_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.193, Running = 0.258, Post = 0.057, Total = 0.508 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.762 0.244     -2.240   -1.762     -1.284 -1.762   0
## vandix_z     0.560 0.203      0.161    0.560      0.959  0.560   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                      mean       sd 0.025quant 0.5quant 0.975quant   mode
## Precision for ui 19965.61 19942.78     615.43 13915.78   73997.84 263.87
## 
## Deviance Information Criterion (DIC) ...............: 130.22
## Deviance Information Criterion (DIC, saturated) ....: 93.75
## Effective number of parameters .....................: 1.97
## 
## Watanabe-Akaike information criterion (WAIC) ...: 130.74
## Effective number of parameters .................: 2.42
## 
## Marginal log-Likelihood:  -68.93 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.8, Running = 0.372, Post = 0.132, Total = 15.3 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.985 0.351     -2.765   -1.955     -1.375 -1.903   0
## vandix_z     0.601 0.231      0.158    0.597      1.069  0.597   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                    mean     sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 12.678 37.455      0.779    4.312     78.077 1.436
## Phi for ui        0.293  0.228      0.018    0.233      0.826 0.045
## 
## Deviance Information Criterion (DIC) ...............: 124.27
## Deviance Information Criterion (DIC, saturated) ....: 87.80
## Effective number of parameters .....................: 9.36
## 
## Watanabe-Akaike information criterion (WAIC) ...: 132.28
## Effective number of parameters .................: 15.04
## 
## Marginal log-Likelihood:  11.10 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 15.2, Running = 0.422, Post = 0.124, Total = 15.8 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -2.423 0.438     -3.340   -2.405     -1.612 -2.406   0
## vandix_z       0.748 0.249      0.264    0.746      1.244  0.746   0
## ln_roads_km_c  0.444 0.244     -0.034    0.443      0.926  0.443   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                    mean      sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 56.460 364.636      0.765    7.786    382.821 1.522
## Phi for ui        0.361   0.247      0.028    0.314      0.881 0.081
## 
## Deviance Information Criterion (DIC) ...............: 123.57
## Deviance Information Criterion (DIC, saturated) ....: 87.10
## Effective number of parameters .....................: 9.93
## 
## Watanabe-Akaike information criterion (WAIC) ...: 128.08
## Effective number of parameters .................: 12.62
## 
## Marginal log-Likelihood:  8.21 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14, Running = 0.353, Post = 0.124, Total = 14.5 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -0.837 0.613     -2.054   -0.833      0.351
## vandix_z                       0.822 0.252      0.331    0.821      1.318
## ln_roads_km_c                  0.197 0.374     -0.536    0.197      0.930
## roads_prop_highway_arterial_z  0.315 0.333     -0.335    0.314      0.970
## ale_index_z                    1.874 1.367     -0.795    1.869      4.570
## canbics_index_z                0.194 1.303     -2.362    0.194      2.750
## population_100_c               0.276 0.095      0.090    0.276      0.464
##                                 mode kld
## (Intercept)                   -0.834   0
## vandix_z                       0.821   0
## ln_roads_km_c                  0.197   0
## roads_prop_highway_arterial_z  0.314   0
## ale_index_z                    1.870   0
## canbics_index_z                0.194   0
## population_100_c               0.276   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                      mean       sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 8350.731 2.26e+05      0.919   69.312   2.86e+04 0.935
## Phi for ui          0.356 2.63e-01      0.019    0.297   9.06e-01 0.043
## 
## Deviance Information Criterion (DIC) ...............: 120.52
## Deviance Information Criterion (DIC, saturated) ....: 84.06
## Effective number of parameters .....................: 8.01
## 
## Watanabe-Akaike information criterion (WAIC) ...: 124.56
## Effective number of parameters .................: 10.46
## 
## Marginal log-Likelihood:  -1.92 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

southeast_models_3 <- cma_models(southeast_sp@data,"Southeast","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
southeast_pedestrian <- clean_fixed_effects(southeast_models_3$fixed_effects)

map(southeast_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.163, Running = 0.225, Post = 0.0685, Total = 0.456 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode   kld
## (Intercept) -2.131 0.446     -3.145   -2.083     -1.405 -2.025 0.010
## vandix_z     0.616 0.276      0.093    0.617      1.149  0.610 0.006
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.529 0.206      0.233    0.494       1.03 0.434
## 
## Deviance Information Criterion (DIC) ...............: 170.46
## Deviance Information Criterion (DIC, saturated) ....: 110.33
## Effective number of parameters .....................: 39.29
## 
## Watanabe-Akaike information criterion (WAIC) ...: 191.49
## Effective number of parameters .................: 39.30
## 
## Marginal log-Likelihood:  -106.80 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.8, Running = 0.379, Post = 0.133, Total = 15.3 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.838 0.317     -2.525   -1.822     -1.262 -1.778   0
## vandix_z     0.529 0.240      0.060    0.528      1.004  0.528   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.734 0.246      0.370    0.695      1.325 0.623
## Phi for ui       0.176 0.148      0.013    0.132      0.565 0.035
## 
## Deviance Information Criterion (DIC) ...............: 167.16
## Deviance Information Criterion (DIC, saturated) ....: 106.98
## Effective number of parameters .....................: 32.57
## 
## Watanabe-Akaike information criterion (WAIC) ...: 170.59
## Effective number of parameters .................: 26.06
## 
## Marginal log-Likelihood:  -24.37 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 14.6, Running = 0.377, Post = 0.134, Total = 15.1 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -2.056 0.378     -2.852   -2.040     -1.358 -2.041   0
## vandix_z       0.574 0.246      0.091    0.573      1.059  0.573   0
## ln_roads_km_c  0.267 0.259     -0.242    0.267      0.779  0.267   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.753 0.260      0.372    0.710      1.382 0.632
## Phi for ui       0.214 0.171      0.016    0.166      0.647 0.044
## 
## Deviance Information Criterion (DIC) ...............: 168.33
## Deviance Information Criterion (DIC, saturated) ....: 108.15
## Effective number of parameters .....................: 32.48
## 
## Watanabe-Akaike information criterion (WAIC) ...: 172.48
## Effective number of parameters .................: 26.56
## 
## Marginal log-Likelihood:  -28.68 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14.7, Running = 0.397, Post = 0.156, Total = 15.3 
## Fixed effects:
##                                 mean    sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -1.262 0.802     -2.886   -1.246      0.272
## vandix_z                       0.581 0.253      0.085    0.581      1.082
## ln_roads_km_c                 -0.061 0.387     -0.829   -0.059      0.693
## roads_prop_highway_arterial_z  0.297 0.332     -0.359    0.298      0.948
## ale_index_z                    0.576 1.430     -2.258    0.584      3.368
## canbics_index_z                0.058 1.490     -2.834    0.044      3.032
## population_100_c               0.213 0.118     -0.015    0.212      0.448
##                                 mode kld
## (Intercept)                   -1.247   0
## vandix_z                       0.581   0
## ln_roads_km_c                 -0.059   0
## roads_prop_highway_arterial_z  0.298   0
## ale_index_z                    0.584   0
## canbics_index_z                0.044   0
## population_100_c               0.212   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.728 0.266      0.346    0.683      1.376 0.600
## Phi for ui       0.241 0.184      0.019    0.193      0.695 0.054
## 
## Deviance Information Criterion (DIC) ...............: 169.90
## Deviance Information Criterion (DIC, saturated) ....: 109.71
## Effective number of parameters .....................: 33.91
## 
## Watanabe-Akaike information criterion (WAIC) ...: 177.56
## Effective number of parameters .................: 29.59
## 
## Marginal log-Likelihood:  -43.62 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
southeast_results <- bind_rows(southeast_all %>% mutate(Region = "Southeast",Outcome = "All Injury Claims"),
                         southeast_cyclist %>% mutate(Region = "Southeast",Outcome = "Cyclist Injury Claims"),
                         southeast_pedestrian %>% mutate(Region = "Southeast",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

Northwest

Descriptive Statistics

region

variable

n

sum

mean

sd

min

max

missing

n_zero

p_zero

Northwest

n_claims

75

4,580.0

61.1

107.4

0.0

746.0

0

3

4.0

n_casualty_claims

498.0

6.6

12.0

0.0

67.0

0

14

18.7

n_cyclist_claims

18.0

0.2

0.7

0.0

3.0

0

64

85.3

n_cyclist_casualty_claims

9.0

0.1

0.4

0.0

2.0

0

67

89.3

n_pedestrian_claims

51.0

0.7

1.2

0.0

5.0

0

51

68.0

n_pedestrian_casualty_claims

41.0

0.5

1.1

0.0

5.0

0

54

72.0

population

32,421.0

432.3

138.7

0.0

747.0

0

1

1.3

total_roads_km

1,124.4

15.0

30.2

0.9

151.7

0

0

0.0

roads_prop_highway_arterial

11.7

0.2

0.2

0.0

1.0

0

36

48.0

no_highschool_prevalance

17.4

0.2

0.1

0.1

0.5

2

0

0.0

unemployment_rate

856.2

11.7

8.1

0.0

44.4

2

4

5.3

hh_avg_income

5,317,156.0

74,889.5

16,545.8

43,382.0

115,632.0

4

0

0.0

participation_rate

4,990.6

68.4

6.6

50.0

81.4

2

0

0.0

university_degree_prevalance

33.9

0.5

0.1

0.2

0.6

2

0

0.0

lone_parent_fam_prevalence

14.1

0.2

0.1

0.0

0.4

2

0

0.0

home_owner_prevalence

50.9

0.7

0.2

0.2

1.0

2

0

0.0

vandix

45.3

0.6

0.9

-0.7

3.4

4

0

0.0

ale_index

-106.5

-1.5

0.5

-2.1

-0.5

3

0

0.0

canbics_index

0.0

0.0

0.0

0.0

0.0

2

73

97.3

Maps

claims <- ggplot() + 
  geom_sf(data = northwest_sf, aes(fill = n_casualty_claims,colour=n_casualty_claims)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Insurance Claims",
                     type = "aggregation", palette = "Earth", direction = -1) + 
  theme_void() + 
  ggtitle(
    "Vancouver"
  )


vandix <- ggplot() + 
  geom_sf(data = northwest_sf, aes(fill = vandix_z_c,colour=vandix_z_c)) +
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  scale_colour_carto_d(name = "VanDIX Score ",
                     type = "diverging", palette = "Earth", direction = -1) + 
  theme_void()


total_roads <- ggplot() + 
  geom_sf(data = northwest_sf, aes(fill = total_roads_km,colour=total_roads_km)) + 
  coord_sf(crs = "+proj=utm +zone=10 +datum=NAD83 +units=m +no_defs") + 
  scale_fill_carto_c(name = "Kilometres of Road",
                     type = "quantitative", palette = "Earth", direction = -1) + 
  scale_colour_carto_c(name = "Kilometres of Road",
                       type = "quantitative", palette = "Earth", direction = -1) + 
  theme_void()

cowplot::plot_grid(claims,vandix,total_roads,ncol=1)

Setting up Spatial Weights Matrix

#### Define Spatial Neighrbourhoods

northwest_sp <- as(northwest_sf, "Spatial")
northwest_sp$ui <- 1:nrow(northwest_sp@data)

coords <- coordinates(northwest_sp)
northwest_nb <- poly2nb(northwest_sp, queen = TRUE)

northwest_nb
## Neighbour list object:
## Number of regions: 75 
## Number of nonzero links: 400 
## Percentage nonzero weights: 7.111111 
## Average number of links: 5.333333
#assign nearest neighbour for no links

northwest_nb <- assign_nearest_neighbors(northwest_nb,northwest_sp)

plot(northwest_sp, border = grey(0.5))
plot(northwest_nb,
     coords = coords,
     add = TRUE, pch = 16, lwd = 2)

Spatial Dependency in each crash type

listw <- nb2listw(northwest_nb,zero.policy = TRUE)
all_cc_mi <- moran.test(northwest_sf$n_casualty_claims, listw,zero.policy = TRUE)
all_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  northwest_sf$n_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 4.4875, p-value = 3.604e-06
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.278584187      -0.013513514       0.004236974
cyc_cc_mi <- moran.test(northwest_sf$n_cyclist_casualty_claims, listw,zero.policy = TRUE)
cyc_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  northwest_sf$n_cyclist_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 1.1222, p-value = 0.1309
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.061319124      -0.013513514       0.004446537
pd_cc_mi <- moran.test(northwest_sf$n_pedestrian_casualty_claims, listw,zero.policy = TRUE)
pd_cc_mi
## 
##  Moran I test under randomisation
## 
## data:  northwest_sf$n_pedestrian_casualty_claims  
## weights: listw    
## 
## Moran I statistic standard deviate = 4.3514, p-value = 6.764e-06
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic       Expectation          Variance 
##       0.288989227      -0.013513514       0.004832834

BYM2 Models

nb2INLA("northwest.adj", northwest_nb)
g <- inla.read.graph(filename = "northwest.adj")


# Model Set 1: Total Casualty Claim Crashes

northwest_models_1 <- cma_models(northwest_sp@data, "Northwest", "n_casualty_claims", "vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
northwest_all <- clean_fixed_effects(northwest_models_1$fixed_effects)

map(northwest_models_1$models, ~ summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.205, Running = 0.216, Post = 0.0613, Total = 0.482 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 0.693 0.216      0.252    0.699      1.101 0.699   0
## vandix_z    0.344 0.121      0.109    0.343      0.586 0.343   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant mode
## Precision for ui 0.694 0.159      0.428    0.679       1.05 0.65
## 
## Deviance Information Criterion (DIC) ...............: 347.02
## Deviance Information Criterion (DIC, saturated) ....: 143.51
## Effective number of parameters .....................: 59.57
## 
## Watanabe-Akaike information criterion (WAIC) ...: 352.20
## Effective number of parameters .................: 44.57
## 
## Marginal log-Likelihood:  -227.05 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.1, Running = 0.328, Post = 0.14, Total = 14.6 
## Fixed effects:
##              mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept) 0.728 0.200      0.321    0.733      1.106 0.733   0
## vandix_z    0.338 0.119      0.106    0.338      0.574 0.338   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.759 0.171      0.480    0.741      1.148 0.704
## Phi for ui       0.162 0.164      0.004    0.102      0.611 0.007
## 
## Deviance Information Criterion (DIC) ...............: 349.00
## Deviance Information Criterion (DIC, saturated) ....: 145.49
## Effective number of parameters .....................: 59.26
## 
## Watanabe-Akaike information criterion (WAIC) ...: 355.39
## Effective number of parameters .................: 45.31
## 
## Marginal log-Likelihood:  -186.79 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 13.5, Running = 0.341, Post = 0.131, Total = 13.9 
## Fixed effects:
##                mean    sd 0.025quant 0.5quant 0.975quant  mode kld
## (Intercept)   0.308 0.215     -0.125    0.312      0.719 0.311   0
## vandix_z      0.388 0.117      0.162    0.387      0.621 0.387   0
## ln_roads_km_c 0.688 0.169      0.354    0.688      1.020 0.689   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 0.678 0.191      0.375    0.654      1.119 0.610
## Phi for ui       0.651 0.212      0.195    0.685      0.957 0.846
## 
## Deviance Information Criterion (DIC) ...............: 338.58
## Deviance Information Criterion (DIC, saturated) ....: 135.07
## Effective number of parameters .....................: 54.79
## 
## Watanabe-Akaike information criterion (WAIC) ...: 339.42
## Effective number of parameters .................: 38.99
## 
## Marginal log-Likelihood:  -184.39 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 13.6, Running = 0.346, Post = 0.114, Total = 14 
## Fixed effects:
##                                 mean     sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -4.533 10.107    -24.606   -4.185     13.837
## vandix_z                       0.274  0.107      0.067    0.274      0.483
## ln_roads_km_c                  0.376  0.296     -0.166    0.368      0.939
## roads_prop_highway_arterial_z  0.241  0.215     -0.183    0.241      0.665
## ale_index_z                    3.285  0.886      1.540    3.286      5.024
## canbics_index_z               -8.760 11.642    -30.041   -9.146     14.587
## population_100_c               0.406  0.120      0.172    0.406      0.641
##                                 mode   kld
## (Intercept)                   -4.415 0.000
## vandix_z                       0.264 0.183
## ln_roads_km_c                  0.385 0.037
## roads_prop_highway_arterial_z  0.203 1.076
## ale_index_z                    3.389 0.359
## canbics_index_z               -8.912 0.000
## population_100_c               0.422 0.509
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.247 0.293      0.766    1.214      1.914 1.153
## Phi for ui       0.121 0.145      0.003    0.064      0.553 0.005
## 
## Deviance Information Criterion (DIC) ...............: -1.35e+18
## Deviance Information Criterion (DIC, saturated) ....: -1.35e+18
## Effective number of parameters .....................: -1.35e+18
## 
## Watanabe-Akaike information criterion (WAIC) ...: 237747.15
## Effective number of parameters .................: 118741.79
## 
## Marginal log-Likelihood:  -185.74 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 2: Total Casualty Cyclist Claim Crashes

northwest_models_2 <- cma_models(northwest_sp@data,"Northwest","n_cyclist_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
northwest_cyclist <- clean_fixed_effects(northwest_models_2$fixed_effects)

map(northwest_models_2$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.191, Running = 0.209, Post = 0.0609, Total = 0.461 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -2.579 0.480     -3.519   -2.579     -1.638 -2.579   0
## vandix_z     0.279 0.218     -0.149    0.279      0.707  0.279   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                      mean       sd 0.025quant 0.5quant 0.975quant   mode
## Precision for ui 19994.34 19947.32     627.83 13945.10   74031.50 274.65
## 
## Deviance Information Criterion (DIC) ...............: 59.78
## Deviance Information Criterion (DIC, saturated) ....: 43.07
## Effective number of parameters .....................: 1.92
## 
## Watanabe-Akaike information criterion (WAIC) ...: 59.97
## Effective number of parameters .................: 1.95
## 
## Marginal log-Likelihood:  -33.15 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 14.2, Running = 0.294, Post = 0.136, Total = 14.6 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -2.606 0.484     -3.558   -2.605     -1.658 -2.605   0
## vandix_z     0.282 0.220     -0.150    0.282      0.715  0.282   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                      mean       sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1257.688 14184.56      2.356   85.806   7909.690 3.599
## Phi for ui          0.341     0.28      0.009    0.264      0.927 0.011
## 
## Deviance Information Criterion (DIC) ...............: 59.70
## Deviance Information Criterion (DIC, saturated) ....: 42.99
## Effective number of parameters .....................: 2.28
## 
## Watanabe-Akaike information criterion (WAIC) ...: 59.92
## Effective number of parameters .................: 2.42
## 
## Marginal log-Likelihood:  4.29 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 14.2, Running = 0.3, Post = 0.149, Total = 14.7 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -2.657 0.542     -3.723   -2.657     -1.596 -2.657   0
## vandix_z       0.291 0.230     -0.160    0.291      0.743  0.291   0
## ln_roads_km_c -0.058 0.357     -0.757   -0.058      0.642 -0.058   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                     mean       sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1276.40 1.46e+04      2.320   85.232   7995.673 3.528
## Phi for ui          0.34 2.81e-01      0.009    0.264      0.927 0.011
## 
## Deviance Information Criterion (DIC) ...............: 61.64
## Deviance Information Criterion (DIC, saturated) ....: 44.93
## Effective number of parameters .....................: 3.17
## 
## Watanabe-Akaike information criterion (WAIC) ...: 62.01
## Effective number of parameters .................: 3.33
## 
## Marginal log-Likelihood:  -0.191 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 14, Running = 0.337, Post = 0.198, Total = 14.5 
## Fixed effects:
##                                  mean     sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -38.517 37.252   -109.947  -35.376     13.733
## vandix_z                       -0.019  0.346     -0.853    0.011      0.574
## ln_roads_km_c                  -1.659  1.668     -5.446   -1.128      0.494
## roads_prop_highway_arterial_z   0.788  0.706     -0.620    0.789      2.191
## ale_index_z                     3.288  3.457     -4.596    3.336     10.010
## canbics_index_z               -45.597 43.289   -128.707  -40.491     14.788
## population_100_c                0.804  0.573     -0.032    0.675      2.157
##                                 mode   kld
## (Intercept)                   -4.198 0.000
## vandix_z                       0.054 0.000
## ln_roads_km_c                 -0.858 0.001
## roads_prop_highway_arterial_z  0.789 0.000
## ale_index_z                    3.273 0.000
## canbics_index_z               -5.864 0.000
## population_100_c               0.543 0.000
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                      mean       sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1375.819 1.62e+04      2.382   86.967   8522.574 3.671
## Phi for ui          0.341 2.81e-01      0.009    0.264      0.927 0.011
## 
## Deviance Information Criterion (DIC) ...............: 102.80
## Deviance Information Criterion (DIC, saturated) ....: 86.09
## Effective number of parameters .....................: 23.20
## 
## Watanabe-Akaike information criterion (WAIC) ...: 708.61
## Effective number of parameters .................: 328.06
## 
## Marginal log-Likelihood:  -9.88 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
# Model Set 3: Total Casualty Cyclist Claim Crashes

northwest_models_3 <- cma_models(northwest_sp@data,"Northwest","n_pedestrian_casualty_claims","vandix_z") 
## [1] "Fit unadjusted non-spatial"
## [1] "Fit unadjusted"
## [1] "Fit adjusted by road length"
## [1] "Fit adjusted by road length and covariates"
northwest_pedestrian <- clean_fixed_effects(northwest_models_3$fixed_effects)

map(northwest_models_3$models,~summary(.x))
## $Nonspatial
## Time used:
##     Pre = 0.216, Running = 0.211, Post = 0.054, Total = 0.481 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.054 0.229     -1.503   -1.054     -0.606 -1.054   0
## vandix_z     0.330 0.101      0.132    0.330      0.528  0.330   0
## 
## Random effects:
##   Name     Model
##     ui IID model
## 
## Model hyperparameters:
##                      mean       sd 0.025quant 0.5quant 0.975quant   mode
## Precision for ui 19915.13 19935.61     594.13 13864.63   73936.99 223.84
## 
## Deviance Information Criterion (DIC) ...............: 162.75
## Deviance Information Criterion (DIC, saturated) ....: 110.89
## Effective number of parameters .....................: 1.98
## 
## Watanabe-Akaike information criterion (WAIC) ...: 164.64
## Effective number of parameters .................: 3.59
## 
## Marginal log-Likelihood:  -86.16 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Unadjusted
## Time used:
##     Pre = 13.4, Running = 0.329, Post = 0.112, Total = 13.8 
## Fixed effects:
##               mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept) -1.430 0.345     -2.169   -1.411     -0.810 -1.360   0
## vandix_z     0.309 0.147      0.023    0.307      0.605  0.307   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.765 1.098      0.557    1.486      4.667 1.083
## Phi for ui       0.303 0.224      0.021    0.249      0.817 0.058
## 
## Deviance Information Criterion (DIC) ...............: 140.66
## Deviance Information Criterion (DIC, saturated) ....: 88.80
## Effective number of parameters .....................: 18.53
## 
## Watanabe-Akaike information criterion (WAIC) ...: 145.84
## Effective number of parameters .................: 18.51
## 
## Marginal log-Likelihood:  -45.69 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted1
## Time used:
##     Pre = 13.3, Running = 0.328, Post = 0.544, Total = 14.2 
## Fixed effects:
##                 mean    sd 0.025quant 0.5quant 0.975quant   mode kld
## (Intercept)   -1.612 0.397     -2.457   -1.592     -0.890 -1.534   0
## vandix_z       0.333 0.154      0.035    0.331      0.642  0.331   0
## ln_roads_km_c  0.207 0.234     -0.242    0.203      0.680  0.203   0
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 1.582 0.958      0.507    1.341       4.11 0.989
## Phi for ui       0.387 0.249      0.033    0.349       0.89 0.103
## 
## Deviance Information Criterion (DIC) ...............: 139.92
## Deviance Information Criterion (DIC, saturated) ....: 88.06
## Effective number of parameters .....................: 19.74
## 
## Watanabe-Akaike information criterion (WAIC) ...: 144.56
## Effective number of parameters .................: 18.85
## 
## Marginal log-Likelihood:  -50.22 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
## 
## 
## $Adjusted2
## Time used:
##     Pre = 13.3, Running = 0.354, Post = 0.12, Total = 13.8 
## Fixed effects:
##                                  mean     sd 0.025quant 0.5quant 0.975quant
## (Intercept)                   -19.299 32.477    -99.203   -7.360     14.678
## vandix_z                        0.413  0.838     -0.160    0.228      3.463
## ln_roads_km_c                  -0.580  2.448     -9.532    0.037      0.999
## roads_prop_highway_arterial_z   0.788  1.741     -0.446    0.333      7.202
## ale_index_z                     6.223  7.345      1.132    4.180     32.923
## canbics_index_z               -20.333 29.636   -101.264  -11.251     14.317
## population_100_c                0.324  0.724     -1.856    0.350      2.077
##                                 mode   kld
## (Intercept)                   -4.269 0.000
## vandix_z                       0.215 0.000
## ln_roads_km_c                  0.023 0.001
## roads_prop_highway_arterial_z  0.344 0.000
## ale_index_z                    4.305 0.000
## canbics_index_z               -6.957 0.000
## population_100_c               0.328 0.000
## 
## Random effects:
##   Name     Model
##     ui BYM2 model
## 
## Model hyperparameters:
##                   mean    sd 0.025quant 0.5quant 0.975quant  mode
## Precision for ui 2.401 1.812      0.625     1.90      7.233 1.268
## Phi for ui       0.285 0.216      0.019     0.23      0.794 0.052
## 
## Deviance Information Criterion (DIC) ...............: -6.59e+24
## Deviance Information Criterion (DIC, saturated) ....: -6.59e+24
## Effective number of parameters .....................: -6.59e+24
## 
## Watanabe-Akaike information criterion (WAIC) ...: 38338.17
## Effective number of parameters .................: 19113.96
## 
## Marginal log-Likelihood:  -57.38 
## CPO, PIT is computed 
## Posterior summaries for the linear predictor and the fitted values are computed
## (Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')
northwest_results <- bind_rows(northwest_all %>% mutate(Region = "Northwest",Outcome = "All Injury Claims"),
                         northwest_cyclist %>% mutate(Region = "Northwest",Outcome = "Cyclist Injury Claims"),
                         northwest_pedestrian %>% mutate(Region = "Northwest",Outcome = "Pedestrian Injury Claims")
                         ) %>%
  filter(variable == "vandix_z") %>%
  select(Region,Outcome,everything())

beepr::beep(8)

Results

Study Area

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Regional Grouping of Census Metropolitan and Agglomeration Areas. Labelled Points Represent Census Metroplitan Area and Census Agglomeration Centroids

Regional Grouping of Census Metropolitan and Agglomeration Areas. Labelled Points Represent Census Metroplitan Area and Census Agglomeration Centroids

Number of DAs

population_mean

Population (%)

Total Roads (km) (%)

Percentage of Major Roads (SD)

Total Injury Claims (%)

Injury Claims Mean (SD)

Total Cycling Injury Claims (%)

Cycling Injury Claims Mean (SD)

Total Pedestrian Injury Claims (%)

Pedestrian Injury Claims Mean (SD)

VANDIX Mean (SD)

No Highschool Prevalence Mean (SD)

Unemployment Rate Mean (SD)

Average Household Income Mean (SD)

Participation Rate Mean (SD)

University Degree Prevalence Mean (SD)

Lone Parent Family Prevalence Mean (SD)

Home Ownership Prevalence Mean (SD)

ALE Index Mean (SD)

CANBICS Index Mean (SD)

6,473

691.9711

4,477,053 (100%)

47,866 (100%)

14.6 (17.4)

211,852 (100%)

32.7 (71)

7,287 (100%)

1.13 (2.77)

10,531 (100%)

1.63 (3.46)

-0.017 (0.64)

0.157 (0.0802)

6.73 (4.57)

80100 (30400)

63.8 (10.9)

0.547 (0.118)

0.16 (0.0787)

0.691 (0.222)

0.693 (3.07)

3.15 (3.65)

The analysis included 6473 dissemination areas across 20 different metropolitan regions with a total of 211852 motor-vehicle crashes resulting in at least one injury, and 7287 such crashes involved at least one cyclist, while 10531 involved at least one pedestrian.

region_name

Number of DAs

Population (%)

Total Roads (km) (%)

Percentage of Major Roads (SD)

Total Injury Claims (%)

Injury Claims Mean (SD)

Total Cycling Injury Claims (%)

Cycling Injury Claims Mean (SD)

Total Pedestrian Injury Claims (%)

Pedestrian Injury Claims Mean (SD)

VANDIX Mean (SD)

No Highschool Prevalence Mean (SD)

Unemployment Rate Mean (SD)

Average Household Income Mean (SD)

Participation Rate Mean (SD)

University Degree Prevalence Mean (SD)

Lone Parent Family Prevalence Mean (SD)

Home Ownership Prevalence Mean (SD)

ALE Index Mean (SD)

CANBICS Index Mean (SD)

Vancouver-Squamish

3,620

2,667,057 (59.6%)

15,057 (31.5%)

15.9 (18.4)

149,692 (70.7%)

41.4 (84.8)

4,968 (68.2%)

1.37 (3.24)

7,502 (71.2%)

2.07 (4.02)

-0.14 (0.58)

0.143 (0.0767)

5.88 (3.58)

85400 (34200)

64.9 (10.1)

0.569 (0.121)

0.155 (0.0659)

0.671 (0.23)

1.63 (3.58)

4.57 (4.11)

Victoria

579

397,237 (8.87%)

3,262 (6.81%)

11.6 (14)

12,338 (5.82%)

21.3 (34.3)

1,027 (14.1%)

1.77 (3.18)

715 (6.79%)

1.23 (2.54)

-0.24 (0.52)

0.121 (0.0581)

5.63 (3.87)

77300 (26900)

63.6 (11.1)

0.597 (0.0978)

0.153 (0.08)

0.654 (0.231)

0.607 (1.78)

2.12 (1.71)

Central Island-Powell River

601

357,163 (7.98%)

5,653 (11.8%)

13 (16.1)

10,762 (5.08%)

17.9 (28.4)

271 (3.72%)

0.451 (0.944)

547 (5.19%)

0.91 (1.97)

0.2 (0.65)

0.177 (0.0756)

8.35 (5.15)

65700 (17200)

56.5 (11)

0.524 (0.0938)

0.167 (0.0948)

0.744 (0.188)

-1.07 (0.719)

0.588 (0.914)

Okanagan

464

336,628 (7.52%)

4,760 (9.94%)

13 (16.2)

13,236 (6.25%)

28.5 (66.7)

485 (6.66%)

1.05 (2.34)

564 (5.36%)

1.22 (3.24)

0.12 (0.6)

0.164 (0.0651)

7.76 (4.73)

73000 (26800)

61.3 (12.9)

0.527 (0.0836)

0.158 (0.0831)

0.728 (0.208)

-0.843 (0.959)

1.9 (1.81)

Fraser Valley

472

309,493 (6.91%)

3,679 (7.69%)

8.58 (13.8)

15,730 (7.42%)

33.3 (65.2)

360 (4.94%)

0.763 (1.58)

725 (6.88%)

1.54 (2.96)

0.31 (0.6)

0.216 (0.0773)

7.05 (5.06)

75400 (21100)

63.6 (11.6)

0.444 (0.088)

0.166 (0.101)

0.741 (0.172)

-0.24 (1.73)

1.39 (1.3)

North Central

350

182,780 (4.08%)

9,990 (20.9%)

13 (14.5)

4,490 (2.12%)

12.8 (25.4)

54 (0.741%)

0.154 (0.55)

203 (1.93%)

0.58 (1.64)

0.5 (0.71)

0.227 (0.0863)

10.5 (6.84)

77700 (21900)

67.9 (9.34)

0.453 (0.0895)

0.182 (0.1)

0.711 (0.236)

-1.32 (0.637)

0.582 (0.981)

Kamloops-Salmon Arm

204

133,847 (2.99%)

2,745 (5.73%)

24.5 (19)

4,069 (1.92%)

19.9 (39.5)

89 (1.22%)

0.436 (1.06)

183 (1.74%)

0.897 (2.28)

0.18 (0.67)

0.17 (0.0717)

8.32 (5.27)

71500 (20400)

62.3 (9.95)

0.511 (0.0944)

0.178 (0.101)

0.74 (0.201)

-0.714 (1.22)

1.4 (1.47)

Southeast

108

60,427 (1.35%)

1,599 (3.34%)

12.8 (15.6)

1,037 (0.489%)

9.6 (17.9)

24 (0.329%)

0.222 (0.616)

51 (0.484%)

0.472 (1.24)

0.079 (0.58)

0.156 (0.0625)

8.06 (4.35)

68700 (16800)

62.2 (8.54)

0.549 (0.0921)

0.165 (0.0835)

0.743 (0.203)

-1.24 (0.743)

0.321 (0.535)

Northwest

75

32,421 (0.724%)

1,125 (2.35%)

15.6 (22.3)

498 (0.235%)

6.64 (12)

9 (0.124%)

0.12 (0.366)

41 (0.389%)

0.547 (1.07)

0.64 (0.85)

0.239 (0.083)

11.7 (8.09)

74900 (16500)

68.4 (6.63)

0.464 (0.0953)

0.193 (0.0932)

0.698 (0.191)

-1.48 (0.48)

0 (0)

Association between Deprivation Index and Traffic Injury

Crude Rates

All Motor Vehicle Traffic Injury Crashes

Bicycle-Motor Vehicle Traffic Injury Crashes

Pedestrian-Motor Vehicle Traffic Injury Crashes

Spatial Models

All Motor Vehicle Traffic Injury Crashes

Regional associations between VanDIX score and number of motor-vehicle crash insurance claims from 2019-2023 fit with nonspatial and spatial models and different covariate values.

Variable

Region

Nonspatial Unadjusted IRR (95% CI)b

Spatial Unadjusted IRR (95% CI)c

Spatial Minimally Adjusted IRR (95% CI)d

Spatial Adjusted IRR (95% CI)e

VanDIX (SD)

Vancouver-Squamish

1.5 (1.42, 1.58)

1.23 (1.15, 1.31)

1.37 (1.3, 1.44)

1.24 (1.19, 1.29)

Victoria

1.59 (1.4, 1.81)

1.21 (1.07, 1.38)

1.37 (1.24, 1.52)

1.21 (1.1, 1.34)

Central Island-Powell River

1.39 (1.24, 1.54)

1.34 (1.19, 1.5)

1.52 (1.37, 1.68)

1.37 (1.25, 1.49)

Okanagan

1.56 (1.32, 1.83)

1.39 (1.16, 1.66)

1.55 (1.34, 1.79)

1.4 (1.23, 1.59)

Fraser Valley

1.4 (1.22, 1.61)

1.23 (1.05, 1.45)

1.31 (1.16, 1.49)

1.14 (1.02, 1.28)

North Central

1.34 (1.16, 1.55)

1.18 (1.02, 1.37)

1.28 (1.11, 1.47)

1.19 (1.05, 1.36)

Kamloops-Salmon Arm

1.46 (1.19, 1.79)

1.28 (1.02, 1.6)

1.28 (1.05, 1.57)

1.22 (1.03, 1.44)

Southeast

1.65 (1.24, 2.19)

1.44 (1.07, 1.92)

1.48 (1.13, 1.96)

1.44 (1.12, 1.87)

Northwest

1.41 (1.12, 1.8)

1.4 (1.11, 1.78)

1.47 (1.18, 1.86)

1.32 (1.07, 1.62)

SD = Standard Deviation; IRR = Incidence Rate Ratio; CI = Credible Interval

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Bicycle-Motor Vehicle Traffic Injury Crashes

Regional associations between VanDIX score and number of motor-vehicle crash insurance claims involving a cyclist from 2019-2023 fit with nonspatial and spatial models and different covariate values.

Variable

Region

Nonspatial Unadjusted IRR (95% CI)b

Spatial Unadjusted IRR (95% CI)c

Spatial Minimally Adjusted IRR (95% CI)d

Spatial Adjusted IRR (95% CI)e

VanDIX (SD)

Vancouver-Squamish

1.03 (0.966, 1.1)

1.15 (1.07, 1.24)

1.23 (1.16, 1.31)

1.2 (1.12, 1.27)

Victoria

1.33 (1.13, 1.56)

1.15 (0.974, 1.37)

1.27 (1.09, 1.49)

1.12 (0.955, 1.31)

Central Island-Powell River

1.32 (1.15, 1.52)

1.37 (1.18, 1.58)

1.45 (1.25, 1.68)

1.4 (1.2, 1.62)

Okanagan

1.94 (1.59, 2.39)

1.86 (1.5, 2.3)

1.97 (1.61, 2.42)

1.72 (1.42, 2.1)

Fraser Valley

1.52 (1.26, 1.84)

1.37 (1.1, 1.71)

1.31 (1.05, 1.63)

1.07 (0.863, 1.33)

North Central

1.27 (1.03, 1.57)

1.32 (1.01, 1.73)

1.36 (1.03, 1.81)

1.36 (1.02, 1.81)

Kamloops-Salmon Arm

1.58 (1.2, 2.09)

1.43 (1.05, 1.93)

1.46 (1.05, 2)

1.45 (1.02, 2.03)

Southeast

1.75 (1.17, 2.61)

1.82 (1.17, 2.91)

2.11 (1.3, 3.47)

2.27 (1.39, 3.74)

Northwest

1.32 (0.862, 2.03)

1.33 (0.861, 2.04)

1.34 (0.852, 2.1)

0.981 (0.426, 1.78)

SD = Standard Deviation; IRR = Incidence Rate Ratio; CI = Credible Interval

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrian-Motor Vehicle Traffic Injury Crashes

Regional associations between VanDIX score and number of motor-vehicle crash insurance claims involving a pedestrian from 2019-2023 fit with nonspatial and spatial models and different covariate values.

Variable

Region

Nonspatial Unadjusted IRR (95% CI)b

Spatial Unadjusted IRR (95% CI)c

Spatial Minimally Adjusted IRR (95% CI)d

Spatial Adjusted IRR (95% CI)e

VanDIX (SD)

Vancouver-Squamish

1.43 (1.35, 1.51)

1.28 (1.19, 1.38)

1.34 (1.25, 1.42)

1.29 (1.22, 1.37)

Victoria

1.61 (1.37, 1.9)

1.41 (1.19, 1.66)

1.56 (1.33, 1.83)

1.36 (1.16, 1.6)

Central Island-Powell River

1.68 (1.45, 1.94)

1.69 (1.45, 1.97)

1.78 (1.53, 2.08)

1.64 (1.42, 1.89)

Okanagan

1.86 (1.53, 2.29)

1.91 (1.53, 2.37)

2 (1.59, 2.52)

1.7 (1.37, 2.12)

Fraser Valley

1.76 (1.5, 2.07)

1.62 (1.35, 1.95)

1.54 (1.29, 1.84)

1.31 (1.11, 1.55)

North Central

1.53 (1.26, 1.87)

1.42 (1.16, 1.74)

1.43 (1.16, 1.76)

1.35 (1.1, 1.66)

Kamloops-Salmon Arm

1.99 (1.49, 2.68)

1.91 (1.4, 2.62)

1.98 (1.45, 2.72)

1.93 (1.43, 2.6)

Southeast

1.85 (1.1, 3.15)

1.7 (1.06, 2.73)

1.77 (1.1, 2.88)

1.79 (1.09, 2.95)

Northwest

1.39 (1.14, 1.7)

1.36 (1.02, 1.83)

1.39 (1.04, 1.9)

1.51 (0.853, 31.9)

SD = Standard Deviation; IRR = Incidence Rate Ratio; CI = Credible Interval

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Supplementary Material

Model Details

Vancouver Model Details

All

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All Motor Vehicle Claims for Vancouver Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

2.850 (2.800, 2.900)

2.800 (2.770, 2.840)

3.250 (3.220, 3.280)

2.990 (2.960, 3.020)

vandix_z

0.407 (0.354, 0.460)

0.204 (0.139, 0.269)

0.315 (0.264, 0.366)

0.216 (0.174, 0.258)

ln_roads_km_c

1.290 (1.230, 1.350)

0.987 (0.934, 1.040)

roads_prop_highway_arterial_z

0.595 (0.563, 0.626)

ale_index_z

0.111 (0.037, 0.184)

canbics_index_z

0.210 (0.137, 0.282)

population_100_c

0.017 (0.012, 0.022)

Hyper Parameters

Precision for ui

0.536 (0.508, 0.564)

0.311 (0.285, 0.340)

0.507 (0.469, 0.547)

0.838 (0.766, 0.915)

Phi for ui

0.793 (0.749, 0.832)

0.810 (0.777, 0.840)

0.777 (0.732, 0.817)

Model Comparison Metrics

WAIC

23973.6

23708.9

23512.6

23292

CPO

52802.5

51800.4

49153.3

43649.3

DIC

23972.2

23815

23704.6

23557.7

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist - Motor Vehicle Claims for Vancouver Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-0.616 (-0.704, -0.534)

-0.522 (-0.587, -0.459)

-0.134 (-0.185, -0.083)

-0.291 (-0.352, -0.231)

vandix_z

0.028 (-0.035, 0.091)

0.142 (0.069, 0.216)

0.209 (0.146, 0.272)

0.180 (0.118, 0.243)

ln_roads_km_c

1.070 (1.000, 1.140)

0.843 (0.766, 0.920)

roads_prop_highway_arterial_z

0.302 (0.256, 0.349)

ale_index_z

0.042 (-0.047, 0.130)

canbics_index_z

0.092 (-0.001, 0.185)

population_100_c

0.022 (0.016, 0.028)

Hyper Parameters

Precision for ui

0.632 (0.577, 0.690)

0.567 (0.489, 0.654)

0.621 (0.532, 0.715)

0.820 (0.688, 0.963)

Phi for ui

0.633 (0.534, 0.724)

0.934 (0.876, 0.974)

0.871 (0.788, 0.934)

Model Comparison Metrics

WAIC

12145.9

9983.1

9017.6

8896.7

CPO

76390.8

66742.6

33974.7

25599.4

DIC

10994.4

9763.2

9035.6

8931.1

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for Vancouver Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-0.020 (-0.082, 0.041)

-0.034 (-0.088, 0.019)

0.319 (0.275, 0.363)

0.114 (0.060, 0.168)

vandix_z

0.358 (0.302, 0.415)

0.249 (0.178, 0.320)

0.289 (0.227, 0.352)

0.257 (0.197, 0.317)

ln_roads_km_c

0.995 (0.928, 1.060)

0.715 (0.639, 0.791)

roads_prop_highway_arterial_z

0.396 (0.353, 0.440)

ale_index_z

0.232 (0.142, 0.323)

canbics_index_z

0.041 (-0.051, 0.134)

population_100_c

0.027 (0.021, 0.034)

Hyper Parameters

Precision for ui

0.716 (0.659, 0.776)

0.493 (0.428, 0.564)

0.448 (0.395, 0.503)

0.707 (0.598, 0.827)

Phi for ui

0.666 (0.576, 0.748)

0.951 (0.908, 0.979)

0.853 (0.767, 0.918)

Model Comparison Metrics

WAIC

13203.4

12268.6

11152.8

10986.4

CPO

74043.9

67190.3

57062.8

40133.7

DIC

12538.9

11937.3

11177.2

11048.3

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Victoria Model Details

All

All Motor Vehicle Claims for Victoria Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

2.450 (2.340, 2.560)

2.350 (2.280, 2.420)

2.370 (2.320, 2.420)

2.530 (2.440, 2.620)

vandix_z

0.464 (0.334, 0.595)

0.191 (0.064, 0.320)

0.315 (0.212, 0.419)

0.193 (0.095, 0.291)

ln_roads_km_c

1.220 (1.080, 1.370)

0.992 (0.835, 1.150)

roads_prop_highway_arterial_z

0.468 (0.373, 0.564)

ale_index_z

0.433 (0.105, 0.761)

canbics_index_z

0.370 (0.064, 0.676)

population_100_c

0.014 (-0.002, 0.031)

Hyper Parameters

Precision for ui

0.698 (0.607, 0.798)

0.472 (0.373, 0.582)

0.606 (0.516, 0.704)

0.816 (0.650, 0.992)

Phi for ui

0.861 (0.727, 0.950)

0.982 (0.934, 0.999)

0.943 (0.833, 0.992)

Model Comparison Metrics

WAIC

3540

3443

3336.3

3339.9

CPO

9258.9

8800.7

7638.8

7087.3

DIC

3529.6

3472.6

3403.1

3399.4

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist- Motor Vehicle Claims for Victoria Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-0.089 (-0.252, 0.065)

-0.132 (-0.274, 0.003)

-0.133 (-0.263, -0.007)

0.053 (-0.106, 0.207)

vandix_z

0.283 (0.123, 0.445)

0.142 (-0.026, 0.311)

0.239 (0.082, 0.396)

0.111 (-0.046, 0.269)

ln_roads_km_c

1.090 (0.866, 1.320)

0.882 (0.629, 1.130)

roads_prop_highway_arterial_z

0.309 (0.167, 0.452)

ale_index_z

0.400 (-0.033, 0.835)

canbics_index_z

0.604 (0.187, 1.020)

population_100_c

0.030 (0.004, 0.058)

Hyper Parameters

Precision for ui

0.719 (0.577, 0.884)

0.663 (0.495, 0.867)

0.635 (0.465, 0.835)

0.845 (0.598, 1.150)

Phi for ui

0.625 (0.414, 0.808)

0.901 (0.740, 0.983)

0.821 (0.601, 0.955)

Model Comparison Metrics

WAIC

1886.3

1758.5

1685.8

1680.3

CPO

11150.4

11027.6

11392.9

9794.9

DIC

1844.3

1756.8

1693.8

1686.2

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for Victoria Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-0.400 (-0.576, -0.235)

-0.428 (-0.578, -0.284)

-0.417 (-0.560, -0.279)

-0.297 (-0.477, -0.125)

vandix_z

0.476 (0.314, 0.641)

0.343 (0.177, 0.509)

0.442 (0.282, 0.602)

0.311 (0.150, 0.471)

ln_roads_km_c

0.847 (0.617, 1.080)

0.571 (0.306, 0.837)

roads_prop_highway_arterial_z

0.386 (0.232, 0.542)

ale_index_z

0.543 (0.083, 1.010)

canbics_index_z

0.343 (-0.120, 0.802)

population_100_c

0.036 (0.009, 0.064)

Hyper Parameters

Precision for ui

0.778 (0.608, 0.981)

0.609 (0.437, 0.821)

0.587 (0.433, 0.775)

0.724 (0.515, 0.981)

Phi for ui

0.794 (0.571, 0.939)

0.951 (0.828, 0.996)

0.924 (0.745, 0.993)

Model Comparison Metrics

WAIC

1578.2

1477.1

1430

1418.9

CPO

10705.2

11593.9

10116.4

9015.4

DIC

1562.2

1480.5

1439.7

1426.6

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Central Island - Powell River Model Details

All

All Motor Vehicle Claims for Central Island - Powell River Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

1.970 (1.850, 2.080)

1.980 (1.880, 2.080)

1.440 (1.320, 1.560)

2.110 (1.880, 2.340)

vandix_z

0.326 (0.218, 0.434)

0.290 (0.173, 0.407)

0.418 (0.315, 0.521)

0.313 (0.225, 0.402)

ln_roads_km_c

0.971 (0.835, 1.110)

0.619 (0.476, 0.763)

roads_prop_highway_arterial_z

0.662 (0.569, 0.755)

ale_index_z

1.430 (0.957, 1.910)

canbics_index_z

-0.657 (-1.110, -0.211)

population_100_c

0.063 (0.037, 0.089)

Hyper Parameters

Precision for ui

0.633 (0.550, 0.723)

0.474 (0.357, 0.622)

0.484 (0.377, 0.615)

0.768 (0.596, 0.973)

Phi for ui

0.478 (0.271, 0.684)

0.684 (0.544, 0.801)

0.648 (0.503, 0.775)

Model Comparison Metrics

WAIC

3560.3

3543.6

3444.1

3391.5

CPO

10011.6

9920.9

9543.7

9167.3

DIC

3525.7

3515.8

3456.6

3426.2

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist- Motor Vehicle Claims for Central Island - Powell River Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.390 (-1.630, -1.180)

-1.400 (-1.620, -1.190)

-1.680 (-1.960, -1.420)

-1.050 (-1.460, -0.651)

vandix_z

0.280 (0.139, 0.421)

0.314 (0.169, 0.459)

0.374 (0.227, 0.521)

0.334 (0.186, 0.482)

ln_roads_km_c

0.475 (0.249, 0.705)

0.277 (0.008, 0.548)

roads_prop_highway_arterial_z

0.426 (0.267, 0.587)

ale_index_z

1.180 (0.385, 1.990)

canbics_index_z

-0.239 (-0.959, 0.475)

population_100_c

0.056 (0.010, 0.103)

Hyper Parameters

Precision for ui

1.190 (0.806, 1.730)

1.080 (0.689, 1.640)

0.948 (0.574, 1.500)

1.220 (0.719, 1.970)

Phi for ui

0.311 (0.080, 0.624)

0.532 (0.229, 0.812)

0.466 (0.174, 0.765)

Model Comparison Metrics

WAIC

1013.3

1004.5

991

968.8

CPO

11028.9

10258.4

10650.8

9047.9

DIC

1019

1008.2

991.7

968.3

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for Central Island - Powell River Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.240 (-1.500, -1.010)

-1.210 (-1.450, -0.999)

-1.540 (-1.820, -1.280)

-0.644 (-1.060, -0.249)

vandix_z

0.517 (0.372, 0.665)

0.524 (0.375, 0.676)

0.578 (0.425, 0.733)

0.494 (0.349, 0.639)

ln_roads_km_c

0.614 (0.361, 0.870)

0.308 (0.037, 0.581)

roads_prop_highway_arterial_z

0.549 (0.391, 0.710)

ale_index_z

2.410 (1.650, 3.180)

canbics_index_z

-1.070 (-1.760, -0.387)

population_100_c

0.112 (0.068, 0.157)

Hyper Parameters

Precision for ui

0.631 (0.483, 0.810)

0.607 (0.441, 0.831)

0.470 (0.302, 0.709)

0.765 (0.504, 1.140)

Phi for ui

0.206 (0.032, 0.502)

0.578 (0.281, 0.827)

0.423 (0.150, 0.718)

Model Comparison Metrics

WAIC

1400.2

1371.9

1324.3

1262.5

CPO

11797.9

12231.5

18441.3

13155.7

DIC

1367.1

1351.3

1312.3

1262.7

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Okanagan Model Details

All

All Motor Vehicle Claims for Okanagan Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

2.180 (2.030, 2.320)

2.180 (2.090, 2.270)

1.600 (1.490, 1.700)

1.990 (1.820, 2.150)

vandix_z

0.442 (0.279, 0.607)

0.329 (0.151, 0.507)

0.438 (0.294, 0.582)

0.336 (0.210, 0.462)

ln_roads_km_c

1.140 (0.993, 1.280)

0.949 (0.800, 1.100)

roads_prop_highway_arterial_z

0.599 (0.492, 0.706)

ale_index_z

0.536 (0.020, 1.050)

canbics_index_z

0.032 (-0.390, 0.454)

population_100_c

0.030 (0.014, 0.047)

Hyper Parameters

Precision for ui

0.471 (0.402, 0.546)

0.240 (0.175, 0.320)

0.243 (0.200, 0.287)

0.341 (0.271, 0.415)

Phi for ui

0.842 (0.705, 0.932)

0.985 (0.949, 0.999)

0.979 (0.927, 0.998)

Model Comparison Metrics

WAIC

2859.1

2779.9

2649.6

2639.8

CPO

7400.5

7268.9

6683.9

6352.8

DIC

2820.1

2778

2701.5

2692.2

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist- Motor Vehicle Claims for Okanagan Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.110 (-1.390, -0.857)

-1.100 (-1.330, -0.893)

-1.490 (-1.770, -1.220)

-0.989 (-1.320, -0.673)

vandix_z

0.665 (0.467, 0.870)

0.618 (0.408, 0.832)

0.676 (0.474, 0.882)

0.545 (0.351, 0.741)

ln_roads_km_c

0.711 (0.474, 0.951)

0.612 (0.344, 0.882)

roads_prop_highway_arterial_z

0.396 (0.222, 0.570)

ale_index_z

0.730 (-0.014, 1.480)

canbics_index_z

0.361 (-0.214, 0.934)

population_100_c

0.036 (0.008, 0.065)

Hyper Parameters

Precision for ui

0.591 (0.440, 0.776)

0.416 (0.263, 0.617)

0.333 (0.228, 0.465)

0.424 (0.286, 0.601)

Phi for ui

0.799 (0.582, 0.937)

0.954 (0.847, 0.995)

0.962 (0.862, 0.997)

Model Comparison Metrics

WAIC

1142.8

993.4

957.6

945.7

CPO

9192.8

11257.1

11818

9456.2

DIC

1108

994.9

964.4

951.8

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for Okanagan Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.060 (-1.340, -0.819)

-1.030 (-1.270, -0.813)

-1.430 (-1.710, -1.160)

-0.836 (-1.160, -0.530)

vandix_z

0.623 (0.423, 0.827)

0.645 (0.428, 0.861)

0.693 (0.462, 0.925)

0.532 (0.314, 0.750)

ln_roads_km_c

0.803 (0.537, 1.070)

0.634 (0.339, 0.930)

roads_prop_highway_arterial_z

0.574 (0.403, 0.748)

ale_index_z

1.330 (0.565, 2.100)

canbics_index_z

-0.240 (-0.875, 0.390)

population_100_c

0.049 (0.018, 0.080)

Hyper Parameters

Precision for ui

0.554 (0.421, 0.712)

0.515 (0.365, 0.710)

0.357 (0.224, 0.536)

0.494 (0.299, 0.767)

Phi for ui

0.346 (0.133, 0.610)

0.770 (0.518, 0.932)

0.722 (0.422, 0.920)

Model Comparison Metrics

WAIC

1197.1

1131.6

1069.3

1034.4

CPO

9296.5

9648.6

13388.4

11549.8

DIC

1152

1113.5

1069.2

1039.4

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Fraser Valley Model Details

All

All Motor Vehicle Claims for Fraser Valley Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

2.470 (2.330, 2.600)

2.480 (2.410, 2.560)

2.270 (2.190, 2.350)

2.720 (2.610, 2.840)

vandix_z

0.335 (0.195, 0.476)

0.210 (0.047, 0.373)

0.273 (0.145, 0.400)

0.132 (0.017, 0.247)

ln_roads_km_c

1.110 (0.973, 1.240)

0.863 (0.722, 1.000)

roads_prop_highway_arterial_z

0.581 (0.466, 0.697)

ale_index_z

0.249 (0.001, 0.498)

canbics_index_z

0.181 (-0.099, 0.456)

population_100_c

0.026 (0.002, 0.051)

Hyper Parameters

Precision for ui

0.604 (0.520, 0.696)

0.282 (0.243, 0.325)

0.708 (0.583, 0.852)

0.951 (0.758, 1.170)

Phi for ui

1.000 (1.000, 1.000)

0.804 (0.683, 0.894)

0.806 (0.657, 0.914)

Model Comparison Metrics

WAIC

3030.9

2957.1

2950.4

2931.1

CPO

7254.7

8745.1

6611.3

6177.7

DIC

3035.4

2989.2

2985.1

2973.4

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist- Motor Vehicle Claims for Fraser Valley Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.270 (-1.550, -1.010)

-1.210 (-1.470, -0.976)

-1.350 (-1.600, -1.120)

-0.785 (-1.080, -0.508)

vandix_z

0.419 (0.231, 0.609)

0.316 (0.094, 0.535)

0.267 (0.047, 0.487)

0.070 (-0.147, 0.284)

ln_roads_km_c

0.756 (0.509, 1.010)

0.468 (0.208, 0.732)

roads_prop_highway_arterial_z

0.603 (0.406, 0.802)

ale_index_z

0.698 (0.279, 1.120)

canbics_index_z

0.092 (-0.495, 0.678)

population_100_c

0.046 (0.001, 0.091)

Hyper Parameters

Precision for ui

0.707 (0.515, 0.949)

0.672 (0.481, 0.921)

0.617 (0.423, 0.865)

0.893 (0.585, 1.310)

Phi for ui

0.326 (0.108, 0.600)

0.758 (0.486, 0.937)

0.615 (0.283, 0.883)

Model Comparison Metrics

WAIC

1022.8

1004.1

964.8

942.3

CPO

8967.5

12422.2

18263

13200.9

DIC

1013.4

998.1

960.7

941.6

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for Fraser Valley Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-0.600 (-0.807, -0.406)

-0.577 (-0.770, -0.395)

-0.723 (-0.906, -0.545)

-0.205 (-0.431, 0.014)

vandix_z

0.566 (0.408, 0.727)

0.485 (0.302, 0.669)

0.431 (0.255, 0.608)

0.270 (0.102, 0.438)

ln_roads_km_c

0.815 (0.610, 1.020)

0.422 (0.199, 0.646)

roads_prop_highway_arterial_z

0.622 (0.461, 0.784)

ale_index_z

0.494 (0.146, 0.842)

canbics_index_z

0.021 (-0.449, 0.489)

population_100_c

0.059 (0.022, 0.097)

Hyper Parameters

Precision for ui

0.781 (0.605, 0.992)

0.733 (0.552, 0.956)

0.654 (0.473, 0.873)

1.040 (0.730, 1.440)

Phi for ui

0.381 (0.174, 0.617)

0.856 (0.646, 0.971)

0.678 (0.395, 0.893)

Model Comparison Metrics

WAIC

1389.4

1354.3

1294.1

1265

CPO

8725.1

10940.6

13480.6

10571.3

DIC

1374.3

1347.5

1296.1

1271.8

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

North Central Model Details

All

All Motor Vehicle Claims for North Central Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

1.390 (1.190, 1.580)

1.440 (1.280, 1.600)

0.699 (0.433, 0.960)

1.200 (0.754, 1.630)

vandix_z

0.294 (0.153, 0.436)

0.166 (0.021, 0.312)

0.246 (0.108, 0.385)

0.177 (0.048, 0.306)

ln_roads_km_c

0.656 (0.474, 0.839)

0.497 (0.321, 0.672)

roads_prop_highway_arterial_z

0.631 (0.463, 0.800)

ale_index_z

-0.204 (-0.780, 0.375)

canbics_index_z

0.429 (-0.183, 1.040)

population_100_c

0.034 (-0.007, 0.077)

Hyper Parameters

Precision for ui

0.537 (0.440, 0.645)

0.308 (0.224, 0.412)

0.236 (0.175, 0.304)

0.276 (0.208, 0.354)

Phi for ui

0.774 (0.624, 0.886)

0.943 (0.856, 0.987)

0.955 (0.876, 0.992)

Model Comparison Metrics

WAIC

1926.7

1859.1

1793.4

1779.7

CPO

6163.4

8900.7

14150.6

12615.4

DIC

1877.8

1836.9

1798.5

1791.4

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist- Motor Vehicle Claims for North Central Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-2.100 (-2.450, -1.750)

-3.070 (-3.830, -2.440)

-3.240 (-4.090, -2.500)

-2.310 (-3.320, -1.370)

vandix_z

0.238 (0.027, 0.450)

0.276 (0.011, 0.547)

0.307 (0.029, 0.591)

0.304 (0.022, 0.593)

ln_roads_km_c

0.127 (-0.188, 0.449)

0.171 (-0.174, 0.521)

roads_prop_highway_arterial_z

0.522 (0.141, 0.908)

ale_index_z

-0.216 (-1.610, 1.180)

canbics_index_z

1.980 (0.896, 3.090)

population_100_c

-0.072 (-0.230, 0.085)

Hyper Parameters

Precision for ui

19,900.000 (586.000, 73,900.000)

0.660 (0.352, 1.150)

0.647 (0.344, 1.130)

0.890 (0.417, 1.730)

Phi for ui

0.162 (0.024, 0.449)

0.195 (0.031, 0.516)

0.288 (0.055, 0.663)

Model Comparison Metrics

WAIC

343.9

281.6

281.4

280.1

CPO

172

216697.9

216794.6

180273

DIC

342.5

276.9

276.5

272.4

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for North Central Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.970 (-2.450, -1.570)

-1.860 (-2.270, -1.500)

-1.940 (-2.440, -1.490)

-1.890 (-2.800, -1.050)

vandix_z

0.424 (0.227, 0.627)

0.350 (0.148, 0.553)

0.355 (0.150, 0.563)

0.301 (0.096, 0.509)

ln_roads_km_c

0.071 (-0.195, 0.358)

-0.097 (-0.402, 0.228)

roads_prop_highway_arterial_z

0.659 (0.375, 0.946)

ale_index_z

-1.050 (-2.310, 0.173)

canbics_index_z

0.649 (-0.317, 1.630)

population_100_c

0.018 (-0.069, 0.105)

Hyper Parameters

Precision for ui

0.563 (0.378, 0.802)

0.555 (0.349, 0.847)

0.531 (0.317, 0.843)

0.546 (0.303, 0.909)

Phi for ui

0.357 (0.102, 0.683)

0.415 (0.107, 0.778)

0.528 (0.170, 0.865)

Model Comparison Metrics

WAIC

627.3

592

590.7

578.1

CPO

6798.8

17702.3

19683.2

22481.3

DIC

613.6

589.8

588.2

575.5

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Kamloops-Salmon Arm

All

All Motor Vehicle Claims for Kamloops-Salmon Arm Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

1.940 (1.730, 2.140)

1.950 (1.790, 2.110)

1.430 (1.230, 1.630)

1.130 (0.900, 1.370)

vandix_z

0.379 (0.178, 0.581)

0.244 (0.019, 0.469)

0.249 (0.047, 0.451)

0.199 (0.034, 0.365)

ln_roads_km_c

0.850 (0.643, 1.060)

0.492 (0.303, 0.682)

roads_prop_highway_arterial_z

0.535 (0.425, 0.646)

ale_index_z

0.092 (-0.412, 0.596)

canbics_index_z

-0.709 (-1.200, -0.220)

population_100_c

0.099 (0.062, 0.135)

Hyper Parameters

Precision for ui

0.565 (0.441, 0.708)

0.646 (0.497, 0.824)

0.773 (0.588, 0.996)

1.170 (0.867, 1.530)

Phi for ui

0.421 (0.223, 0.639)

0.627 (0.427, 0.804)

0.820 (0.622, 0.948)

Model Comparison Metrics

WAIC

1199

1181.7

1151.7

1123.5

CPO

3437.7

3381

4627

4126.6

DIC

1187.1

1176.1

1158.3

1138.2

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist- Motor Vehicle Claims for Kamloops-Salmon Arm Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.700 (-2.220, -1.270)

-1.620 (-2.050, -1.230)

-2.040 (-2.620, -1.520)

-1.920 (-2.590, -1.310)

vandix_z

0.456 (0.182, 0.737)

0.358 (0.051, 0.655)

0.376 (0.053, 0.691)

0.372 (0.017, 0.706)

ln_roads_km_c

0.585 (0.198, 0.991)

0.195 (-0.225, 0.626)

roads_prop_highway_arterial_z

0.399 (0.130, 0.673)

ale_index_z

0.639 (-0.333, 1.590)

canbics_index_z

-0.277 (-1.240, 0.693)

population_100_c

0.141 (0.066, 0.217)

Hyper Parameters

Precision for ui

0.921 (0.468, 1.710)

1.050 (0.560, 1.840)

1.050 (0.546, 1.880)

1.810 (0.713, 4.030)

Phi for ui

0.214 (0.035, 0.531)

0.523 (0.162, 0.874)

0.627 (0.180, 0.950)

Model Comparison Metrics

WAIC

326.1

325.4

318.6

311.1

CPO

3803.5

8353.3

15976.5

10699.7

DIC

325

323.3

316.7

308.2

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for Kamloops-Salmon Arm Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.600 (-2.130, -1.160)

-1.460 (-1.890, -1.090)

-1.850 (-2.350, -1.390)

-1.580 (-2.170, -1.030)

vandix_z

0.687 (0.402, 0.988)

0.649 (0.340, 0.964)

0.685 (0.371, 1.000)

0.659 (0.359, 0.957)

ln_roads_km_c

0.619 (0.267, 0.979)

0.245 (-0.124, 0.619)

roads_prop_highway_arterial_z

0.393 (0.152, 0.636)

ale_index_z

1.570 (0.680, 2.450)

canbics_index_z

-0.979 (-1.880, -0.099)

population_100_c

0.111 (0.039, 0.184)

Hyper Parameters

Precision for ui

0.506 (0.316, 0.761)

0.625 (0.404, 0.923)

0.674 (0.425, 1.020)

1.080 (0.602, 1.830)

Phi for ui

0.271 (0.077, 0.552)

0.478 (0.194, 0.781)

0.379 (0.067, 0.786)

Model Comparison Metrics

WAIC

439.8

423.7

414.9

404.6

CPO

12443.2

15490.7

16687.5

10292.4

DIC

421.6

415.6

408.9

400.8

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Southeast

All

All Motor Vehicle Claims for Southeast Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

1.310 (1.040, 1.570)

1.320 (1.100, 1.530)

0.761 (0.435, 1.080)

1.750 (0.950, 2.540)

vandix_z

0.500 (0.219, 0.783)

0.363 (0.072, 0.653)

0.394 (0.121, 0.670)

0.367 (0.112, 0.626)

ln_roads_km_c

0.707 (0.396, 1.020)

0.450 (0.093, 0.813)

roads_prop_highway_arterial_z

0.570 (0.271, 0.868)

ale_index_z

1.650 (0.043, 3.270)

canbics_index_z

-0.567 (-2.250, 1.110)

population_100_c

0.143 (0.028, 0.260)

Hyper Parameters

Precision for ui

0.708 (0.490, 0.976)

0.778 (0.549, 1.070)

0.855 (0.593, 1.190)

1.030 (0.708, 1.440)

Phi for ui

0.387 (0.138, 0.690)

0.643 (0.326, 0.897)

0.679 (0.367, 0.912)

Model Comparison Metrics

WAIC

548.8

543.7

527.6

521.5

CPO

1996.6

1958.9

2617.1

2620.3

DIC

544.6

540.4

530.5

526.6

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist- Motor Vehicle Claims for SoutheastRegion

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.760 (-2.240, -1.280)

-1.980 (-2.770, -1.370)

-2.420 (-3.340, -1.610)

-0.837 (-2.050, 0.351)

vandix_z

0.560 (0.161, 0.959)

0.601 (0.158, 1.070)

0.748 (0.264, 1.240)

0.822 (0.331, 1.320)

ln_roads_km_c

0.444 (-0.034, 0.926)

0.197 (-0.536, 0.930)

roads_prop_highway_arterial_z

0.315 (-0.335, 0.970)

ale_index_z

1.870 (-0.795, 4.570)

canbics_index_z

0.194 (-2.360, 2.750)

population_100_c

0.276 (0.090, 0.464)

Hyper Parameters

Precision for ui

20,000.000 (615.000, 74,000.000)

12.700 (0.779, 78.100)

56.500 (0.765, 383.000)

8,350.000 (0.919, 28,600.000)

Phi for ui

0.293 (0.018, 0.826)

0.361 (0.028, 0.881)

0.356 (0.019, 0.906)

Model Comparison Metrics

WAIC

130.7

132.3

128.1

124.6

CPO

65.4

35855.1

9993.4

8971.5

DIC

130.2

124.3

123.6

120.5

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for Southeast Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-2.130 (-3.140, -1.400)

-1.840 (-2.530, -1.260)

-2.060 (-2.850, -1.360)

-1.260 (-2.890, 0.272)

vandix_z

0.616 (0.093, 1.150)

0.529 (0.060, 1.000)

0.574 (0.091, 1.060)

0.581 (0.085, 1.080)

ln_roads_km_c

0.267 (-0.242, 0.779)

-0.061 (-0.829, 0.693)

roads_prop_highway_arterial_z

0.297 (-0.359, 0.948)

ale_index_z

0.576 (-2.260, 3.370)

canbics_index_z

0.058 (-2.830, 3.030)

population_100_c

0.213 (-0.015, 0.448)

Hyper Parameters

Precision for ui

0.529 (0.233, 1.030)

0.734 (0.370, 1.330)

0.753 (0.372, 1.380)

0.728 (0.346, 1.380)

Phi for ui

0.176 (0.012, 0.565)

0.214 (0.016, 0.647)

0.241 (0.019, 0.695)

Model Comparison Metrics

WAIC

191.5

170.6

172.5

177.6

CPO

59059.2

46976

49599.3

56251

DIC

170.5

167.2

168.3

169.9

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Northwest

All

All Motor Vehicle Claims for Northwest Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

0.693 (0.252, 1.100)

0.728 (0.321, 1.110)

0.308 (-0.125, 0.719)

-4.530 (-24.600, 13.800)

vandix_z

0.344 (0.109, 0.586)

0.338 (0.106, 0.574)

0.388 (0.162, 0.621)

0.274 (0.066, 0.483)

ln_roads_km_c

0.688 (0.354, 1.020)

0.376 (-0.166, 0.939)

roads_prop_highway_arterial_z

0.241 (-0.183, 0.665)

ale_index_z

3.280 (1.540, 5.020)

canbics_index_z

-8.760 (-30.000, 14.600)

population_100_c

0.406 (0.172, 0.641)

Hyper Parameters

Precision for ui

0.694 (0.428, 1.050)

0.759 (0.480, 1.150)

0.678 (0.375, 1.120)

1.250 (0.766, 1.910)

Phi for ui

0.162 (0.004, 0.611)

0.651 (0.195, 0.957)

0.121 (0.003, 0.553)

Model Comparison Metrics

WAIC

352.2

355.4

339.4

237747.2

CPO

1402.9

1420

2089.3

25154.2

DIC

347

349

338.6

-1346432140868630016

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Cyclists

Cyclist- Motor Vehicle Claims for NorthwestRegion

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-2.580 (-3.520, -1.640)

-2.610 (-3.560, -1.660)

-2.660 (-3.720, -1.600)

-38.500 (-110.000, 13.700)

vandix_z

0.279 (-0.149, 0.707)

0.282 (-0.150, 0.715)

0.291 (-0.160, 0.743)

-0.019 (-0.853, 0.574)

ln_roads_km_c

-0.058 (-0.757, 0.642)

-1.660 (-5.450, 0.494)

roads_prop_highway_arterial_z

0.788 (-0.620, 2.190)

ale_index_z

3.290 (-4.600, 10.000)

canbics_index_z

-45.600 (-129.000, 14.800)

population_100_c

0.804 (-0.032, 2.160)

Hyper Parameters

Precision for ui

20,000.000 (628.000, 74,000.000)

1,260.000 (2.360, 7,910.000)

1,280.000 (2.320, 8,000.000)

1,380.000 (2.380, 8,520.000)

Phi for ui

0.341 (0.009, 0.927)

0.340 (0.009, 0.927)

0.341 (0.009, 0.927)

Model Comparison Metrics

WAIC

60

59.9

62

708.6

CPO

44.2

114.8

232.2

4751.9

DIC

59.8

59.7

61.6

102.8

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Pedestrians

Pedestrian - Motor Vehicle Claims for Northwest Region

term

Nonspatialb

Unadjustedc

Adjusted1d

Adjusted2e

Fixed Effects

(Intercept)

-1.050 (-1.500, -0.606)

-1.430 (-2.170, -0.810)

-1.610 (-2.460, -0.890)

-19.300 (-99.200, 14.700)

vandix_z

0.330 (0.132, 0.528)

0.309 (0.023, 0.605)

0.333 (0.035, 0.642)

0.413 (-0.160, 3.460)

ln_roads_km_c

0.207 (-0.242, 0.680)

-0.580 (-9.530, 0.999)

roads_prop_highway_arterial_z

0.788 (-0.446, 7.200)

ale_index_z

6.220 (1.130, 32.900)

canbics_index_z

-20.300 (-101.000, 14.300)

population_100_c

0.324 (-1.860, 2.080)

Hyper Parameters

Precision for ui

19,900.000 (594.000, 73,900.000)

1.770 (0.557, 4.670)

1.580 (0.507, 4.110)

2.400 (0.625, 7.230)

Phi for ui

0.303 (0.021, 0.817)

0.387 (0.033, 0.890)

0.285 (0.019, 0.794)

Model Comparison Metrics

WAIC

164.6

145.8

144.6

38338.2

CPO

83.7

2010.5

2692.3

5511.2

DIC

162.7

140.7

139.9

-6.58997031579091e+24

bFit with idd random effect at dissemination area level

cFit with idd and spatial random effect at dissemination area level

dFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads

eFit with idd and spatial random effect at dissemination area level + adjusted for (i) total length of roads; (ii) proportion of roads classified as highway or arterial; (iii) the Canadian Active Living Environment Index; (iv) the Canadian Bikeway Comfort and Safety Index; (v) total population

Built Environment by VanDIX

  • Of the 9 regions, we observed 5 had on average a positive relationship with deprivation index and the proportion of roads in the neighborhood that were arterial or highway

  • Of the 9 regions, we observed 8 had on average a positive relationship with deprivation index and thactive living environment index score

  • Of the 9 regions, we observed 7 had on average a positive relationship with deprivation index and increased access to better bicycle facilities.

Reproducibility receipt

## [1] "Total run time: 26.3 minutes"
## [1] "2024-10-11 12:15:20 PDT"
## Local:    main C:/Users/micha/Documents/GitHub/Area-Level-Deprivation-Traffic-Injury
## Remote:   main @ origin (https://github.com/mbcalles/Area-Level-Deprivation-Traffic-Injury.git)
## Head:     [29024e1] 2024-10-08: Remove old scripts
## R version 4.4.1 (2024-06-14 ucrt)
## Platform: x86_64-w64-mingw32/x64
## Running under: Windows 11 x64 (build 22631)
## 
## Matrix products: default
## 
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## [5] LC_TIME=English_Canada.utf8    
## 
## time zone: America/Vancouver
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] extrafont_0.19     broom_1.0.7        janitor_2.2.0      cowplot_1.1.3     
##  [5] rcartocolor_2.1.1  RColorBrewer_1.1-3 flextable_0.9.6    spdep_1.3-6       
##  [9] sf_1.0-17          spData_2.3.3       lubridate_1.9.3    forcats_1.0.0     
## [13] stringr_1.5.1      dplyr_1.1.4        purrr_1.0.2        readr_2.1.5       
## [17] tidyr_1.3.1        tibble_3.2.1       ggplot2_3.5.1      tidyverse_2.0.0   
## [21] INLA_24.06.27      sp_2.1-4           Matrix_1.7-0      
## 
## loaded via a namespace (and not attached):
##  [1] DBI_1.2.3               deldir_2.0-4            s2_1.1.7               
##  [4] rlang_1.1.4             magrittr_2.0.3          git2r_0.33.0           
##  [7] hrbrthemes_0.8.7        snakecase_0.11.1        e1071_1.7-16           
## [10] compiler_4.4.1          mgcv_1.9-1              systemfonts_1.1.0      
## [13] vctrs_0.6.5             pkgconfig_2.0.3         wk_0.9.3               
## [16] crayon_1.5.3            fastmap_1.2.0           backports_1.5.0        
## [19] labeling_0.4.3          geojsonsf_2.0.3         utf8_1.2.4             
## [22] rmarkdown_2.28          tzdb_0.4.0              ragg_1.3.3             
## [25] MatrixModels_0.5-3      bit_4.5.0               xfun_0.47              
## [28] cachem_1.1.0            jsonlite_1.8.9          cancensus_0.5.7        
## [31] highr_0.11              uuid_1.2-1              tictoc_1.2.1           
## [34] parallel_4.4.1          R6_2.5.1                bslib_0.8.0            
## [37] stringi_1.8.4           extrafontdb_1.0         boot_1.3-30            
## [40] jquerylib_0.1.4         Rcpp_1.0.13             knitr_1.48             
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## [46] tidyselect_1.2.1        rstudioapi_0.16.0       yaml_2.3.10            
## [49] curl_5.2.3              lattice_0.22-6          withr_3.0.1            
## [52] askpass_1.2.0           evaluate_1.0.0          units_0.8-5            
## [55] proxy_0.4-27            zip_2.3.1               xml2_1.3.6             
## [58] pillar_1.9.0            KernSmooth_2.23-24      generics_0.1.3         
## [61] vroom_1.6.5             hms_1.1.3               munsell_0.5.1          
## [64] scales_1.3.0            class_7.3-22            glue_1.8.0             
## [67] gdtools_0.4.0           tools_4.4.1             data.table_1.16.0      
## [70] beepr_2.0               grid_4.4.1              Rttf2pt1_1.3.12        
## [73] colorspace_2.1-1        nlme_3.1-164            ggspatial_1.1.9        
## [76] cli_3.6.3               textshaping_0.4.0       officer_0.6.6          
## [79] fontBitstreamVera_0.1.1 fansi_1.0.6             fmesher_0.1.7          
## [82] gtable_0.3.5            sass_0.4.9              digest_0.6.37          
## [85] fontquiver_0.2.1        classInt_0.4-10         ggrepel_0.9.6          
## [88] farver_2.1.2            htmltools_0.5.8.1       lifecycle_1.0.4        
## [91] httr_1.4.7              fontLiberation_0.1.0    openssl_2.2.2          
## [94] bit64_4.5.2